Hmm, you may be on to something there, and now my thinking is that it might have something to do with a change in the latest betas and not just these custom channels that we've recently added. I have started to see the "Connection Lost" error, after a period of time watching regular TVE channels, on my AppleTV's Channels DVR client. I never saw this error before, and I've been using Channels for very many hours daily for a few months now. I'm just got the error watching MSNBC for example. Yesterday it happened on ABC. It happened a few times over the past few days and it's not only happening to me with custom channels.
My Channels DVR server is on an always-on, hard-wired iMac and I'm able to resume watching on the client app by exiting to the guide, and selecting the channel again, without changing anything else.
So what could explain this "Connection Lost?" I note that when this happens by LAN is still up and running, I can ping my server, access the web, use other apps on my AppleTV, etc. It's just the Channels client that (for some reason) now intermittently loses connection.