On some game-stopping occasions, it involves the game no longer being fun (which coincides with being boring). The same dungeons over and over again, the same bad guys, the same dragging, really bad story, cut scenes, or script, terribly painful game-play, the whole box of reasons put together. The reasons I put a game down depend entirely on the type of game, itself. There is no one solid game-stopping scenario involving mechanics that would make me quit every game.
Another, more understandable reason I would stop playing a game is if a funner game came out and told me, "Hey, put down that piece of garbage you're currently playing. I'm much, Much better."
An another reason for stopping games involves motion sickness. This involves most first-person shooters. I cannot play a game if I feel like I am going to blow chunks five to ten minutes into it.
Edit - editing my post to make sense.
Another edit - to add another reason.