How does game center manage a match when users close then reopen the game?

For example if they have a text message or call they respond to, then they reactivate the game, how long does game center give them before telling them they are disconnected? Is it possible to change this timeout value? Is it different in sandbox mode vs production?

The timeout will run less than 60 seconds, you cannot change the timeout amount. A non-turned based Game Center game is meant to be played continuously without exiting the app. Exiting the app will end the game, which is by design.