Game Center: doesn't remember me

Hi.

Actually the title is a bit of a lie. I have a new Retina iPad and when I go into Game Center it remembers me and has all my details. I don't need to log in each time.

However my wife has an iPad 2 and she has to log in every time we try to play a game together.

I have searched and can't find any "remember me" settings so I can't understand why mine stays logged in and hers doesn't.

We're both using iOS 6.0.1.

Any help would be appreciated.