I\'m working on a turn based iOS game using the new turn-based iOS5 API.
One of the delegate protocols you need to implement for this is GKTurnBasedEventHandlerDele
As the documentation says, that message is received when the player has accepted the push notification (typically by unlocking the phone or via notification center). Sending push notifications is decided in Game Center client-side, and automatically done for you by GameKit. You don't need to implement a GKTurnBasedEventHandlerDelegate in order for them to work, only to respond to the player accepting them (by automatically returning to that match or whatever).
I guess it's worth double checking in your device's Notification settings to see that your app has Notification Center alerts enabled.