Brian has two Apple TVs that stream music from his computer and iTunes, but lately it just stops after a few minutes. Apple says that it's a corrupted library, but Leo disagrees since it doesn't happen when he streams music on his computer directly. Leo has a hunch it's the router. Using AirPlay, he could be dealing with buffering issues. He also should make sure nothing else is connected to his AirPlay device. It could also be an issue with home sharing and his router configuration. It could be a blocked port issue. Here's an article on MacWorld: "Why Troubleshooting Home Sharing Is so Painful".
Max should be sure everything is updated. He should shut down everything on the network except on Mac and one Apple TV and see what happens. If it doesn't, he's narrowed it down. If it does, he can slowly add everything one at a time and see when it hiccups. The router may need replacing.