This is totally a guess, but I think that the live chess and the correspondence chess might be on different servers (or different sets of servers). I have the chess.com app on my iphone, and I use it for both kinds of play. There was one day though, where could consistently get to the correspondence games, but not to the live games. I got a message saying something to the effect of "could not contact server" when I tried to play live, but was able to go back and forth to the correspondence games whenever I wanted. This lasted for a while. I have no idea if I was right, but after a bit of head scratching, it seemed like the only explanation was the games were being served from different physical boxes.
Maybe the 3.1 OS lacks the ability to make certain types of connections to those servers.
Of course, that doesn't explain why it starts to load and then shuts off. I have that happen with other apps, but usually only after an iOS upgrade. Did you try reinstalling the app?
Just some random thoughts
I downloaded the Chess.com App for my Ipod touch. It is a first G but my ios 3.1 is compatible with the software requirements. Everything else works great but the "Live Chess" wich kind of sucks because thats why I go it. That part of the app begins to load and then just shuts off. Has anyone else had this problem. Any help is much appreciated. Thanks. Ps I know it is not the initial connection to the server because I am able to play the correspondence games with no problems.