Game center invitation failing on 2nd generation ipod touch

I am working on a multiplayer game with connections via Game Center and GKMatch. I have three devices -- a 4th generation iPod touch, a 2nd generation iPod touch, and an iPad 2. Connecting the two newer devices works just fine. But if I try to use the ol开发者_StackOverflowder device to connect one of the newer ones, Apple's default invitation says "want to play (null)?" instead of "want to play ([name of my game])?". And the newer device never gets a message that the older one has invited it.

The older device is running iOS 4.2.1. The newer ones are running iOS 4.3.3.

Inviting the older device with a newer one also fails. The invitation looks correct, but the older device never receives it.

How can I fix that?