Reenabling GameCenter after user-cancelled 3 times (iOS7 only) [duplicate]
General > Reset > Reset All Settings
Thats the only way I've heard of fixing it, hopefully Apple comes up with a more elegant way, because it's downright annoying and absolutely NOT user friendly.
In iOS 6, if you logged out and logged back into GC, it would be re-enabled. But that functionality was removed in iOS 7 for some reason.
Edit:
I read in another SO question, that this works properly (log-out, log-in re-enables GC) outside of a sandbox environment.
I can confirm the following:
On the iPhone Simulator, using Settings, log into your iTunes sandbox account, then log back out. After that, the count will be reset and you can continue testing Game Center view controller authentication.
This is on XCode 5.0.2 and iPhone 4-inch 64-bit Simulator with iOS 7.0.3