It's a matter of perspective for the most part. The key is not "I'm the worst player in the world" or "I'll never get better at this, I suck", but having the desire and believing that you will get better or will learn that one trick that it takes or figuring out the mechanics of the world. In my mind getting better at titles like Super Meat Boy from Super Mario 3D Land or Kirby's Epic Yarn to Volgarr the Viking isn't that far removed, it's me learning the mechanics and learning how to best use them even if I do die often/lose points or time.
A title like Demon's Souls or early Castlevanias or Rayman Legends I see what's coming in front of me and I know I could get there, I just have to learn to react better or figure out the right way to go about it. A title like Mega Man 2 could seem hard with the bosses, but once it's known what they are weak to it's suddenly not so bad for most. The fact it's not "impossible" tells me it can be done, so I keep going for it.
The important key in that though is if I enjoy the game play. I don't actually like Dark Souls due to certain sections, certain enemies, and other issues I won't get into and it simply wasn't fun for me I had to force my way through certain parts of the game and I can't stand that. So even though I could get past areas, I could improve and react better, I didn't want to because it wasn't fun for me to play. A lot of single player FPS on the hardest difficulty setting could be beat I know, but if it's just bullet sponges with cheap A.I., and me with very little health as the "difficulty" than I'm not going to bother because it's no fun for me.
On the other hand Rogue Legacy and FTL I'm always dying and not always improving, but I enjoy playing it still because the game play is fun and that prevents any stress. There is a game on Mega Drive called Death Duel that I have never beat, I'm not sure I will ever be able to beat it, and yet I love playing the game from time to time despite getting stuck at the same enemy every time with no visible improvement.
I enjoy a challenge in games, Save for a few games where I just play to play such as Death Duel or most casual puzzle titles (sudoku, picross, etc) I enjoy being able to say I improved or figured out what the game was throwing at me. Single player or multiplayer, it's a sense of progression in a game even if it's just me being better at it rather than a level bar increasing or percentage going up. If you don't feel that progression any more, if you don't have the sense of "I could get better at this" and most importantly you don't feel like the game play by itself is fun enough to keep going at, than there is no secret or way to get over it and may never be, and that's okay to move on from if it's just not for you.