This has happened to me many times with many games, and I can't even begin to list them all.
Spider-man (2003): I got to a portion of the game where I had to battle The Scorpion down in a sewer. There were mutiple points in the game prior to this where I got stuck for long periods of time. It took me a week just to finish the intro phase of the game because they throw you into the game unclear about what your first objective even is. Then there was a section where I had to battle The Shocker, and that seemed impossible for awhile, but I did beat him eventually. I was still interested in the game because Spiderman was probably one of my favorite Marvel characters, but the game itself was on thin ice for me. I got to that section with The Scorpion and I could not beat him. At that point I had enough. I gave up on the game after numerous attempts to beat The Scorpion.
The Lord of the Rings: The Third Age - As a child The Lord of the Rings films captivated me. I remember my Uncle came home one day and bought it because he thought I would like it. I wanted to like it, but I ended up hating every single thing about it. Seriously, one day I should blog about how much I hated this game. The story sucked, at the time I didn't have much patience for turned-based RPGs, and that's what the combat in this game was. As I got further my dislike grew, until finally I got to a part in the game where Idrail, the elf in the game's party, gets seperated from the group and has to fight some of the Nazgul by herself. The battle was like impossible for me to beat, and I tried to beat it seriously a few times. I couldn't do it.
I was fed up with the whole game by then, it had gotten mind-numbingly repetitive, plus the story was so stupid, so that was the point where I decided to just give up. I put a lot of time into that game though, I was kind of sad it had to end with me hating everything about the game, because before I started playing it, I was so sure I'd like it.