Game Center authentication doesn't appear (error code 2) [257.20]

So I'm just trying out Game Center for the first time, so I might be missing something basic, but I have enabled Game Center on iTunes Connect and was able to login with a sandbox account using iPhone 5. However, on iPod touch 4th gen I seem to be unable to bring up the authentication screen and Xcode shows the following error:

GameCenter Error 2: Error Domain=GKErrorDomain Code=2 "The requested operation has been cancelled." UserInfo=0x1cd82810 {NSLocalizedDescription=The requested operation has been cancelled.}

Any ideas on what might be causing this error?

Hmm.. it should not matter in this case, because the problem is that I can't get the login screen to appear on iPod at all.

Whereas on iPhone 5, GC authentication screen pops up normally, on iPod it does not show at all, so I can't even try logging in to GameCenter on iPod..

Yes, AyreGuitar, I'm logged out of GC on the iPod touch as well when trying to bring up the authentication screen.

You were right: on the iPod touch, GC seemed to be somehow stuck even though I was logged out. After I created a new account (normal one, not sandbox), and logged out of that too, the authentication appears normally. Thanks for the help!