Current Game: Anomaly Warzone Earth
Progress: 10 missions completed

It's really not a bad game (though the attempts by the writers to insist on the Britishness of the characters might lead you to believe otherwise). I totally understand what they're going for, flipping the tower defense genre on its head. Nothing wrong with that, nothing in particular wrong with the execution of that idea, it's just not an idea that inspires any interest from me. Every time I've thought "hey, got a little extra time in my day, I should game" a little voice has said "but you have to play Anomaly . . ." and I've moved on to other things. This is not helping my challenge at all.
So, I'm trying to break it down: Why am I trying to complete this challenge? One of the big reasons it caught my eye is my realization of the large number of games I haven't really given a try. Surely I should be getting my money's worth for all these games. Another reason is experiencing a broader array of artistic endeavors - if all I do is play Civilization and Team Fortress, I'm limiting myself and my understanding of the gaming milieu. And, as with any challenge, there's a certain male boisterousness that inspired some (possibly unwarranted) bravado.

I'll admit, I don't have a hard and fast rule for situations like this. So far, the two games that I've quit prematurely have been at 3 hours. I don't want to make that the standard by any means. But it's been nine days since I finished Amnesia and I've still only mustered up three hours of playtime for Anomaly. Because it's felt like work. The game has led me to cheat on the challenge with The Binding of Isaac, of all things. That game is so hard, I've racked up 10 hours total without coming especially close to the (first) ending.
I've seen this suggestion bandied about on Reddit and I generally like it: Once you complete a game in order, you can select one game out of order that you'd like to play and continue to that. I think the best way for me might actually be to select a game and have that be an option. Having two very different games will help a lot, I think. So, for example: I beat Amnesia, now I've selected Binding as my choice. The next alphabetical option is Audiosurf. I can play either of those and be within the rules of my updated challenge. When I beat the alphabetical game, I move onto the next. When I beat the selected game, I select another. And so on.
This solves the game exhaustion problem, but does not address the possibly more significant problem of games that have utterly failed to inspire. This is a problem that's going to take some thought, and more than likely will end up being on a case-by-case basis. My underlying principle is this: Give the game a genuine, fair shot to the best of my ability.

"Best fireworks display I've seen since Guy Fawkes night!"
"That dome makes Big Ben look like a midget!"
"Keep this up and the Queen will have you over for tea and crumpets!"
Anyway, now I'll switch the progress bit:
Current Games: Audiosurf / The Binding of Isaac
Progress: 3 hours played / 11 hours played