I think he enjoyed his tenure as Wolverine but maybe he believes it is time to move on to explore other interests.
He has not explored as much as he probably wants to in his career.
He would probably like to see other options on the film side ( the only announced major project is APOSTLE PAUL and an Aussie animation project LARRIKINS)he has also been approached for a film adaptation of Homer's classic THE ODYSSEY ( no indication if he is still interested in that). At the moment, in direct contrast to LOGAN, he is now involved in the FOX-produced/distributed movie musical called THE GREATEST SHOWMAN ON EARTH ( with Michelle Williams, Rebecca Ferguson, Zac Efron and Zendaya) which is due for release on Christmas 2017!
He has done well in dramatic movies, including thrillers ( Prisoners, The Prestige, or even an indie-type like The Fountain) so, it is likely that he would like to explore other scripts, which are interesting and can make full use of his drama training. It is likely that future projects will include other action movies, dramas, musicals, even other genres. So, it may not be so much as simply health considerations that is moving him out of the XMEN franchise but also a desire to widen his range further.
He is also a stage actor who is in much demand on Broadway ( or even the West End). Right now, celebrated director Trevor Nunn, has indicated his strong interest in getting Hugh involved in another project in musical theatre ( although Hugh has not expressed interest at the moment - his name is often linked whenever a major stage project is being considered). But it looks like he is also keen to do straight plays ( his last Broadway show in late 2014 was a play called THE RIVER, an enigmatic and reflective work). In the past, he has always said the wants to do a Shakespeare ( part of his training is classical theatre) with mentor Trevor Nunn ( who directed him in two previous stage musicals), so that is another bucket list wish.
I hope that in extended set interviews for LOGAN that someone will explore from him what his career path indications would be. Maybe even ask if he would be willing to do at least a cameo of Wolverine for one last time

Man I wish Marvel had the rights Wolverine in the MCU would be a dream come true.
Lose the Game!!!!!!!

Well I don't think that is likely, plus they will have tons of characters to use already, I am sure they can do without Wolverine for Infinity War.

When Hugh makes a final decision, it's final. He's done - for his health's sake, for his career's sake, and for his family's sake.

im telling you guys if marvel someone gets the right back for his character before Infinity War Part 2 - I could totally see him reprising his role for that film as his send off.

I think he has hung up his wolverine boots for good.

I'm surprised i haven't heard more discussion about this, whether ppl are just hypothesizing or if yhere was actually any real discussion in the mattet amonst the players.
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yes it would