Looks like you have a clear hypothesis here, i.e. That Game Center connections are closed after 30 seconds idle time. I would not be surprised if this is the case.
Other games almost certainly will send data within such an interval, and you may be triggering a timeout condition. To test this hypothesis and fix the problem at the same time, I would send a short blind text every five or ten seconds.
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.