I don't think the problem is so much fatigue with the X-properties. It's just that FOX has no vision. They make every movie almost the same, they waste characters that could headline their own films on cameos only to look pretty or show of a cool special effect, instead of being given any actual character. They pointlessly kill off characters. No thought seems to go into making sure possibilities are kept open and they only look at each movie individually with no thoughts about what future movies could be made.
But it seems they didn't even realize a movie not about Wolverine, Xavier, Magneto or Jennifer Lawrence under the title of "X-Men" or "Wolverine" could even work until Deadpool succeeded. And even then it seems they think it works because it was R-rated and not because it actually took the things that made the source material great. Only now are they starting to make things like New Mutants and X-Force.
If they'd focus on making compelling movies with interesting characters instead of shoving in a bunch of mutants to show of a special effect or look pretty these movies could go on forever. Believe it or not, Emma Frost, Banshee, Polaris, Havok, Kitty Pryde, Jubilee, Psylocke, Northstar, Wolfsbane, Syrin, Cable, Madrox, Magik, Blink, Sunspot, Cannonball, Domino, Warpath, Bishop and many more could be major characters or even main characters if they were used for more than special effects and weren't killed off after one movie. But it seems they can't even do leaders like Cyclops or Storm right, so I guess this will never happen...
For example, if I were at FOX I'd be like "Well, these space movies like Star Wars and Guardians of the Galaxy sure seem popular. We have the rights to a whole bunch of stuff like the Shi'ar, Strontians, Brood, Starjammers, etc. Maybe we could think about doing something like that. The Starjammers seem like the most well suited for a movie, so let's keep our options to do that movie open. Maybe we can't figure it out, but until we know for sure, let's at least not kill off any characters or make it very hard for them to be on this team. All we need to do is make sure Havok lives and we leave the possibility for Corsair and Polaris to appear open and don't make it unnecessarily hard for ourselves to potentially make such a movie."
Do you think they ever even considered they could make succesfull movies out of X-Factor, Excalibur, Exiles, Alpha Flight, Starjammers and a whole bunch of other mutants?