I was having this same issue with an iPad 3 (retina) running iOS7 - evidently in iOS7 if Game Center is dismissed from your app 3 times the user is NEVER prompted again, and there is no way to reset this by re-logging in to Game Center (as you could in iOS6).
The current fix that worked for me is to reset settings - Settings->General->Reset->Reset All Settings.
Hopefully Apple fixes this bug in the next release, or at least provides better Game Center documentation for iOS7.