As I get older, the amount of time I have to play games is becoming less and less. I find that if a game doesn't engage me within the first 1 to 3 hours, it goes on the shelf never to come off again. There are so many games out there (I have roughly 250 on GOG alone) that I want to play, but haven't gotten to yet, that it doesn't bother me. The problem is that I feel a little guilty when I play this awesome game everyone hypes up, only to find out I'm kindof "meh" about it.
i also find that I get interrupted a lot, where I may play for a few hours a day during the week, but then have to go 3-4 days without touching the game. There are a lot of games that, for me anyway, lose their effect if they aren't finished really close to when you started. So the game may have been awesome, but I don't go back to it because it's been so long since I was involved in the story or gameplay.
So for me, the story has to be gripping and the gameplay has to be dynamic or enjoyable enough to want to play the entire length of the game. I find a lot of games get really tedious towards the last 2-3 hours, while I find myself wanting more from others.
TL;DR: It just depends on the game.