I don't know why it became irrelevant in the last 5 years or so.
And long before. The irrelevancy of the Fantastic Four has a long history. Here are some of the milestones as I see them:
Milestones in the 1960sFF 67 ("Him"): the last straw for Kirby. When Lee completely changed the "Him" story, Kirby resolved to not put in as much effort. There are still some magnificent Kirby stories after that, but most people notice the lack of great new characters and tendency to use recycled ideas from TV after that. The FF were still officially "the world's greatest comics magazine" but the relative decline began here. The following year brought The Marvel Explosion, Steranko, and all kinds of then-exciting changes. Spider-man was entrenched as the top character by now. Good will toward the FF was still at its peak, and rightly so, but the slide toward irrelevancy had begun.
FF 102: Kirby left. Among hard core students of the silver age this is probably the event that matters. Nuff said.
Milestones in the 1970s
FF 132-144 (the sadness became entrenched). In 132 Crystal became engaged to Pietro. In 133 Ben began his long career of being a third rate punching bag. In 141 Reed zapped Franklin. While "the FF died here" is a minority view, this marks the end of the joyful optimism that was central to the FF.
FF 200: Reed beats Doom. Although my head chooses a later date, my heart is here. This was the last big, bright, muscular silver age style story. It was a natural ending that even Reed sad he expected to disband the team after that because there was nothing left to do. Later issues had a different and less bombastic tone. For those who dislike Byrne's work 200 is a popular choice for an end to the classic run. Because after 200 (1978) there are 30 issues that many fans see as mediocre. It became popular to say the FF had lost its way, hence Byrne's choice to consciously look backwards and try a soft reboot back to happier times.
Trying to halt the decline: the 1980-1990s
In this period all the cool kids were watching the rise of the X-Men. The X-men rose ever higher, and the FF (apart from the run by X-Men legend Byrne) sank ever lower.
FF 295 (Byrne's last issue): Byrne's run was so popular that probably the majority of older fans see him as the end of the good stuff. But I think that ignores the underlying problems: the problems that people identify after Byrne were all there before him. He bucked the trend simply because he was a top creative talent, given freedom and time, and he really cared. Personally I have a lot of problem with Byrne's run, but he did a lot of very enjoyable stand alone issues.
FF 333 (the end of continuity). This is a minority view! Most fans consider Englehart's run to be problematic, if not mediocre. (Needless to say I disagree!) If continuity matters then 333 is huge. Its importance cannot be overstated. Englehart was the last writer to attempt to move the story forwards. If continuity matters then this is where the series died. I stress that this is small minority view.
FF 353 (Simonson's last) while most people put Byrne as the last "good" writer a significant minority would extend the "good" period a few issues later to include Simonson. It helped that this was followed by the problematic DeFalco run that started with Alicia being declared a skrull. That makes it a huge jumping off point at least in hindsight.
FF 416 (the end of volume 1, at least for a while): if you liked DeFalco's run, and many people do, then this was a natural ending. While the title continued with volume 2, it was clear to everyone that the X-Men had long since eclipsed the FF in popularity, and even the Avengers were considered the hotter team.
Trying to pick up the pieces: The 2000s and beyond
The years that followed brought two acclaimed runs, by Waid and Hickman, but they were consciously trying to fix something that was broken. E.g. Waid got the gig specifically because of his manifesto, where he wrote about what had gone wrong with FF and how he thought it could be fixed.
In short, by the time of Heroes Reborn (1996) the vast majority of fans considered the FF to be has-beens. The FF were the problem child, the sick man of Marvel, the Ottoman Empire, and nothing seemed able to halt their decline.
Finally, the fact that nobody knows what to do with the FF has led to some mediocre movies. This just angers Marvel, and they naturally want the rights back so they can try to do a better job. As a result Marvel will no longer do anything to promote the FF. And that is where we are today, with the FF as the very definition of mediocrity, who only sell because people remember that once, long ago, they were the world's greatest comic magazine.
OK. so that is WHEN they went wrong. But WHY?
It is obvious that the X-Men and Avengers are now more popular, and remain more popular despite wider industry trends and everyday chaos like new writers. So let us look at why. I will outline a number of theories, before saying which I prefer, and why, and what (if anything) can be done.
Theory 1: victims of their own success.
The FF matched the mood of the 1960s so well that nobody would dare change anything. In contrast, the Avengers were not as hot, and did not match the mood quite as closely, so they were open to change. As for the X-Men, hey failed so badly they had to change completely. And Spider-man, while very successful, was not tied to a particular time. But the FF were tied to space race sensibilities and that is over.
Please note that moving forward was not anathema. Kirby was always moving forward. it's not just the marriage and Franklin and Crystal joining the team: Toward he end of the run he was even moving past the emphasis on superpowers. Most of his later stories would work just as well for non-powered folk, and he often showed the later FF in civilian situations. If we want to emulate Kirby then change was pat of the deal. But most writers and artists are not Kirby. His ability to come up with new ideas was perhaps unique. Certainly Lee didn't like change: as soon as Kirby left, so did Crystal, Franklin became a problem, and the team returned to reruns of classic adventures. Change means risk. Kirby's ideas have since been shown to have billion dollar value, but comic companies don't want to nurture new ideas for decades "just in case". Kirby was R&D, but Stan was sales.
Theory 2: bad writersThis leads to the issue of good and bad writing. To their credit, Marvel has always tried to throw their "best" writers at the FF, so that is not the problem. But as soon as the hot writer leaves the interest leaves with them. And some of the "hot" writers simply dis not understand or care for the characters (e.g. Mark Millar).
Also, there is a big problem with Marvel writing in general. We are now in the fourth generation of in-bred writers and editors who only know superheroes. Whereas Kirby could move smoothly between all ages and genres and concepts, modern writers have no concept of anything beyond muscle bound fighters aged 18-34. Occasionally Marvel bring in somebody from TV or movies, but they are from the same narrow world: escapist fiction for 18-34 year olds. Over the last decade the worlds of TV sci-fi and comics has become just one narrow clique. To illustrate, just look at the problem they have writing children. Or old folks. Or anything even remotely real. We have a generation that thinks "adult equals sex" and "realistic means violence." Nothing could be more juvenile.
This works in books featuring just superhero battles. But it is less successful in books featuring families and exploring.
Theory 3: too much change
Byrne's theory was simple: the FF had moved too far from their roots So he did a soft reboot back to 1963. For a while it worked, but you can only keep that up for 5 years or so before fans notice that if nothing ever changes, nothing ever matters. Byrne is quite open about his belief that readers should recycle every 5 years or so. And after 5 years on the book he had nothing new to add, so left.
If we want to void change then we must rely on the illusion of change, and that brings up the next problem:
Theory 4: the illusion of change cannot work for a fixed team.
The illusion of change will work to a degree, for an ever cycling team. There is always a new Avenger or new X-man to fall in love, get killed, etc.,so the soap opera can continue. but when you a have a fixed team the illusion is broken. There is e very limited number of times you can kill a character who must be there every month. fans notice. And worse, if the team has a child who cannot grow up, it becomes a constant reminder than nothing ever changes, that the illusion of change does not work.
Without change, or at least its illusion, there is no story.
Theory 5: victims of their own failure
When the FF's decline was obvious, by the 1990s, they became canon fodder. When a strong character wanted to show he was strong he could just beat The Thing. When Tony Stark wanted to show he was smart he could be on a level with Reed Richards. And if somebody had to do something extremely distasteful, like build a secret prison, Tony was too popular: Reed can do it. This punching bag problem was even true inside the FF: writers felt that Sue had been portrayed as weak, so they made her strong - which meant making Reed come off weak. Naturally I think they are wrong on both the problem and the solution, but for 20 years now Ben has been a whining punching bag and reed has been (until Hickman tried to rescue him) a jerk.
Another way they are victims of their failure is that new writers go back to old writers for their reference. But the old writers don't have a clue either. Generally a new writer will read the first few Kirby issues (which are old and hard to update) and the most recent issues (which are generally failures). So new writers come away with the message "great team [Kirby], lost its way [recent]". But they have no idea what to do. So again and again we see solicits that say in effect "new writer! important team! things will never be the same again!" Yawn, yawn, yawn. Message to Marvel: neither of these things are selling points any more. It just shows you have no ideas.
Theory 6: not enough newWaid's theory was that the FF dd not do enough new things. His solution, his way to get back to the early creativity of the Fantastic Four, was to enforce newness: "EVERY ISSUE of this series should revolve around concepts or notions or scenes or characters you've NEVER SEEN BEFORE in a comic."
A noble aim. But it has two problems. First, it is impossible to be new while permanent change is banned. So nearly everything you do has been done before. Waid's own run illustrates this:
62: a computer program comes to life and attacks them, again (see FF201, or the first Quasimodo story, annual 5)
65: the patents are licensed and it turns out to be a big mistake, again (see FF160).
66. unstable molecules spread. This isn't the first time that unstable molecules have caused problems (see the Mad Thinker's awesome android) but it is the first time they spread in this way. Excellent story! But no long term significance, sadly.
67. Doom has a new costume, Just as he did in Byrne's run, and again in Simonson's run.
68. Franklin is trapped in Hell, Just as he was in Byrne's run.
500 (back to original numbering: nothing ever permanently changes): Reed is scarred. (Last time it was Ben; before that in FF296 it was Johnny)
503: set up democracy in Latveria again (last done in 200)
511: Waid's only genuinely "new" storyline was going to heaven to bring Ben back from the dead. This was certainly new, but it is an obvious story that was previously avoided for an obvious reason: it cheapens death, so poisoning the well for future writers.
516: the Wizard has a previously unknown daughter
518: Manhattan is lifted into the sky again (see FF242) because somebody is hiding from Galactus again (see FF48) and again they Sue has unique powers (see FF242, FF400)
523: Galactus again
524: lose powers again
532: Reed creates the universe. This is a new idea!!!! A pity it's never been referred to since then. Perhaps because, like bringing someone back from heaven, it opens a can of worms and also removes all future drama.
The second problem is that Stan and Jack did not write that way.
Waid wanted to recapture the greatness of Stan and Jack's FF, yet advocated the opposite of what they did. Stan and jack did not try new things, they tried old things, but did them realistically.
Take Galactus for example: world threats were not new. But making us believe in it - that was new.
Or take Waid's favorite story, "This Man, This Monster": stealing powers and noble sacrifices were hardly new. But making us care - that was new.
Waid also mentions the Negative Zone: it's just a sci fi version of a hell gate, familiar from many horror comics. What was new was how they did it.
So how did Stan and Jack do it? We don't need a new manifesto: Stan Lee already gave us his manifesto already. It's in Fantastic Four issue 9 and many other places: "incredible exploits plus down-to-earth realism." But "down to earth realism" is no longer possible after decades of power inflation where every superhero is a billionaire.
Theory 7: the writer does not get their true nature?
Waid said the FF are not superheroes but explorers. Others say they are not a super team but a family. It is a common refrain: "they last writer does not really understand the FF but I do". Superficially this is appealing, but it is problematic. For example, for the first year the FF were not like a family at all (only Sue and Johnny were related, they did not live in the same building, etc.) and in the Lee-Kirby run they did almost no exploring. Well Reed did a little, occasionally, but this buys into the whole myth that the team equals Reed Richards. I think that idea is completely false and does far more damage than any "false" ideas about the team's real nature. In Waid's run for example, everybody was a fifth wheel except Reed, but that's while other topic.
Another problem with the "true nature" theory is that every writer has a different idea. For example, Byrne said tht Simonsons;' run ws "good comics, but not Fantastic Four comics." Personally I feel the same way about Byrne's run and feel that Simonson got closer to the original team than Byrne did, but of course that's just an opinion. Either way I think "true identity" is so fluid and multi layered that this can never be more than a secondary concern.
For what it's worth, I think the "true nature" of the FF is as a monster comic, not a superhero comic. If you want a quick guide to which are good issues and which are mediocre issues, see how big the characters are on the cover. If they look overshadowed by a much larger enemy, it's usually a good issue. if they seem just as powerful as the the enemy (as is the case in superhero comics, which are about feeling powerful), the FF story is usually mediocre. But as I said, that's secondary.
Good grief, I didn't intend such a long reply!
OK, instead of continuing with the problems and synthesizing them, I'll cut to the chase.
The real problemI think the FF is in trouble for essentially two reasons:
1. it was fundamentally a monster comic. That was abandoned. Even if it is brought back, monster comics worked best in the cold war, and that is over.
2. It was a soap opera. Soap operas rely on constant change, and marvel comics is against that on principle.
The solution, in my view
I see two solutions, and they are not mutually exclusive.
1. The easy way: Return to the monster comic roots.
Superheroes are about power fantasies. but monster comics are about feeling ordinary and threatened, yet winning by your wits. So make them more real, and smaller and weaker than their enemies. Scaling back worked for Byrne. You may have to split the FF into its separate reality to do this: as billionaires surrounded by uber-powerful friends they cannot work. The reader must feel the danger they are in. Make every second page (or every second frame if possible) extremely mundane and down to earth, something a low income reader can relate to. Just like Kirby did. You have to relate to the danger.
2. The harder way: think long term profit, not short term sales.
Truly great stories will only make money in the long term. In the short term some readers won't like them, but if the stories have long term depth you can sell them again and again to new generations. Create an epic where real things happen, even though that will mean real change. Make this a soap opera where characters really grow and die and readers really care. Sell the back issues. And have a parallel "classic version" for those who don't want change but just want their favourite eras again and again.
tl;dr the FF is a monster comic + family soap opera. They are not regular superheroes, and soap opera cannot work if change is only an illusion. That is why they fail as superhero comics. IMO