Personally I think he's just no longer invested in it. Winds has a lot of problems in terms of getting plots completed and characters where they need to be for the finale, and he already had to deal with that once in Dance.
He's been cold on it ever since 2011. Winds of Winter should have come out in 2013 or 2014, and the final book should have come out in 2017, earliest. He stopped getting involved when the show was still reaching its stride. The peak of the show was in 2014 when the fourth season came out, he should have finished Winds of Winter by then.
There's also the ridiculous pressure, Winds was at one point probably one of the most hyped books of the century, and that pressure has to have gotten to him.
That pressure used to exist, especially after the last season of the show crashed and burned, but now, there's just apathy. No one cares anymore, outside of the diehards who still think that Martin is some kind of 4D-chess player when really, he's the lesser, hippie-modernist version of Luo Guanzhong or William Shakespeare, nowhere near the literary genius of Tolkien, or those other two authors.
Also fact is it may just be too complex for him to keep track of. There's the main ice zombie plot, the Dany plot, Tyrion's plot, the stark kids, Dorne and Jaimie, Cersei, the fake Aegon, Stannis, and Lady Stoneheart.
That's a big problem. He kept piling on plotline after plotline. There's also the Euron plotline to add to all that mess. The problem with GRRM was that there was no one to reign him in and force him to focus. It's the same problem George Lucas had when during the time when he was writing the Prequels, there was no one to tell him "no". The difference is that Lucas had an outline that he stuck to, which at least allowed him to end the Prequels on a hopeful note, whereas GRRM is just going around his world, following random plotlines, adding to the bloat of the story when he should be chopping things down and getting things to a close.
Like say, whey not have Stannis and Lady Stoneheart join forces with Petyr Baelish and the forces of the Vale? You'd unite three separate plotlines into one, and the three of them have different reasons for wanting to see the Lannisters fall: Stannis has honor, Stoneheart has vengeance, the forces of the Vale hate the Lannisters for supposedly killing Jon Arryn, and Littlefinger's a greedy little shit. That's what I'd do in his position to cut down on the fat and set up a coherent ending.
He has to somehow weave all these plot threads in a coherent and skillful fashion, while also setting up a finale that I believe he has an ending for(if its even 50% the same as the show's I can see why he'd have given up) and also maintain his standard quality as a writer.
Ideally, the sixth and seventh books should see GRRM trying to unite and conclude several different plotlines and set up the final conflict, but he's either incapable or unwilling to do that. I think the show's ending is partially based on his ending, as it does have all the elements and themes of his subversive narrative, albeit rushed to meet an artificial deadline. (In war, there are no good guys, one side's hero is another side's villain, the death caused by war outweighs all the potential good it may cause, etc..) So yeah, part of his hesitance may be due to the show being so poorly-received when it adapted his ending. If D&D had their way, Jon Snow and Dany would just win with their trademark generic good-guy talk, and they'd have just ended up mating on the Iron Throne after the deaths of Cersei and the Night King.
I don't think he'll ever publicly admit to giving up, but I do think he has in fact given up.
I've made my peace with that. Shit, I even made up my own endings from Season 5 onwards, and to me, ASOIAF can go rest in peace without me caring about what GRRM can come up with. Because unless he comes up with the mother of all literary miracles, I doubt he can even finish an ending that's as good as the endings made by the average fan-fic authors.
