I'm going to post here my latest update, paraphrased from my thread in the Apple support forums:
What happens is the ATV syncs for a while, then stops syncing and stops showing up in iTunes. There is no indication of the ATV on the computers under iTunes Preferences. Under Computers on the AppleTV itself, the library appears grayed-out. However, iTunes can still use speakers through the ATV, so in some way it still "sees" the ATV and finds it on the network.
What's more, after playing around with this more, I noticed that I can set up my iTunes library again from "Computers" on the ATV, but it sets it up as a streaming library, and won't sync it. But it does see the computer the same way it might see a second computer in the house that it streams to but doesn't sync to (since it can only sync with one computer at a time). It's like the AppleTV and iMac have forgotten that they know each other and have a syncing relationship, and are back to being mere acquaintances.
That seems to me to be different from a networking glitch. The AppleTV always shows up in the network, always has an IP address, and can always find the internet. What I did learn from this, though, is that I could go ahead and sync the ATV fully and then if I have new media I want to use after the connection disintegrates, I can just stream it. That's a decidedly un-Appley workaround, but it's something at least.
I talked to Apple again and they bumped me up to a more senior support person, since I have now done just about everything anyone can think of. He had me send my computer logs to him and found nothing amiss with the network, etc. His idea was that it might be an issue with the MobileMe syncing. MobileMe was syncing my preferences. The thought is that there might be some messed-up preference somewhere either on the other computer or the cloud, and after I've done things like reinstall iTunes or reinstall the OS, the goofy preference just gets synced right back and messes it up again. The way the MobileMe syncing is set up, you really can't tell what preferences they are syncing and how, so it's at least plausible. It also seems to go along with the intermittent nature of this - when this happens and I resync everything, it can work for a varying period of time, anywhere from hours to days. I don't think MobileMe pushes the preference syncing the same way it does for calendar/contacts, so it is possible it may take a while for both computers to sync to the cloud again and have the bad preference copied over.
I want this to work, partially because there is logic to it and partially because I am really sick of this whole problem. The part about this solution that doesn't make sense to me is that it doesn't seem to explain the many, many posts I've seen of people having AppleTV issues, since there's no way all of those people are using MobileMe. Still, I think it's possible that I had something get goofed up that otherwise would have been fixed by one of these other solutions (connecting by ethernet, reinstalling iTunes, reisntalling the OS, etc.), but it didn't work because the bad file kept getting restored.
Anyway, I will keep you all posted.
What happens is the ATV syncs for a while, then stops syncing and stops showing up in iTunes. There is no indication of the ATV on the computers under iTunes Preferences. Under Computers on the AppleTV itself, the library appears grayed-out. However, iTunes can still use speakers through the ATV, so in some way it still "sees" the ATV and finds it on the network.
What's more, after playing around with this more, I noticed that I can set up my iTunes library again from "Computers" on the ATV, but it sets it up as a streaming library, and won't sync it. But it does see the computer the same way it might see a second computer in the house that it streams to but doesn't sync to (since it can only sync with one computer at a time). It's like the AppleTV and iMac have forgotten that they know each other and have a syncing relationship, and are back to being mere acquaintances.
That seems to me to be different from a networking glitch. The AppleTV always shows up in the network, always has an IP address, and can always find the internet. What I did learn from this, though, is that I could go ahead and sync the ATV fully and then if I have new media I want to use after the connection disintegrates, I can just stream it. That's a decidedly un-Appley workaround, but it's something at least.
I talked to Apple again and they bumped me up to a more senior support person, since I have now done just about everything anyone can think of. He had me send my computer logs to him and found nothing amiss with the network, etc. His idea was that it might be an issue with the MobileMe syncing. MobileMe was syncing my preferences. The thought is that there might be some messed-up preference somewhere either on the other computer or the cloud, and after I've done things like reinstall iTunes or reinstall the OS, the goofy preference just gets synced right back and messes it up again. The way the MobileMe syncing is set up, you really can't tell what preferences they are syncing and how, so it's at least plausible. It also seems to go along with the intermittent nature of this - when this happens and I resync everything, it can work for a varying period of time, anywhere from hours to days. I don't think MobileMe pushes the preference syncing the same way it does for calendar/contacts, so it is possible it may take a while for both computers to sync to the cloud again and have the bad preference copied over.
I want this to work, partially because there is logic to it and partially because I am really sick of this whole problem. The part about this solution that doesn't make sense to me is that it doesn't seem to explain the many, many posts I've seen of people having AppleTV issues, since there's no way all of those people are using MobileMe. Still, I think it's possible that I had something get goofed up that otherwise would have been fixed by one of these other solutions (connecting by ethernet, reinstalling iTunes, reisntalling the OS, etc.), but it didn't work because the bad file kept getting restored.
Anyway, I will keep you all posted.
tv is maintaining it's IP address. Is there any chance that address is getting reassigned by your router and the 
