Pushing a lesbian old growth union-approved agenda since '94.
I have started several multi-player games of Ticket to Ride Pocket and Tigris and Euphrates on my iPhone and the games have appeared in Game Center. Every game I have started or joined ends up being terminated at some point in the future. At first I thought maybe the game had to be completed in one sitting as after being away from the phone awhile the games had disappeared. Then I thought maybe others were cancelling the games from their end.
T&E has a feature where your opponent can delete the game if you haven't moved for 72 hours.
But I think your issues is just that Game Center is flaking out on you. Try power-cycling your phone.