I am also facing the same problem. My game stops accepting turn events and turns notifications from the Game Center, I finished the game and tested, but this week the problem started. It worked like a charm, but suddenly the authorities began not to receive turnaround events for a couple of days.
I use the iOS7 SDK and configure iOS7 (event handling is different from previous versions of iOS, I will need exchanges in upcoming game functions, so I use iOS7).
Then I made a test application to check if it was the same with iOS6 and previous SDKs, but without help, it was the same. Therefore, do not waste time updating your code to iOS7, hoping that this will work, there is a problem. I also tried many things, such as rebooting devices and settings, using new users, etc.
I also tried this with Ray Wenderlich Turn-Based Gaming with the iOS 5 tutorial by downloading the source code and it also doesn't work.
The fact is that when I start the game, the game receives turn events, but after several turns it just stops, and when it stops receiving, it stops as always. If I restart the match, I can get an updated match, and it will also be updated, so I can make a move. This means that the match is being updated in Game Center. Thus, either Game Center does not push data to users (this may be because the user cannot receive notifications from Game Center when the game is in the background), or GameKit does not fire an event for the handler.
I don’t know why this is happening, or why it was starting to happen, but I can’t release my game like this, hoping it works out of the sandbox. I'll try a couple more things (for example, try turning iOS7 reminders to see if they click on the user), then I will ask the Apple support group. Another thing I plan to do is to put the test application on the App Store and see if it works from the sandbox.
Hope this is a sandbox issue.