A post on Zynga's blog says that resignation times are now 11 days without a move for an invite game and 5 days without a move for a random game. (Previous times were 22 days and 7 days, respectively.)
Update: Based on Iszi's comments below, I've done a little more digging and found the following information about the Android version (no idea whether this applies to the iOS version as well):
Q: Some of my games are resigning early. Why?
A: This usually means the data on your app is out of sync with our server. Again, try deleting and reinstalling the app and seeing if the resigned-early games come back.
I can now confirm from personal experience that games do not always take as long as Zynga says to resign. I started an invite game at 8:59 PM Sunday local time and made no moves; when I checked Tuesday at about 10:18 AM local time, I had lost. I have my account set to update every 5 minutes, so it seems as though in this case, my game was resigned in a little over 36 hours. (I also tried deleting and reinstalling the app, and the game did not come back.)