I don't know if this will help anyone or not...
I have 3 AppleTV's in the house. Two are wi-fi, and one with a wired connection. Every time I came to use the AppleTV's (regardless of network connection) I'd have to restart iTunes as per everyone else here.
After reading through this post, I thought I'd try an experiment. Last night, I pulled the ethernet cable from the only wired AppleTV. I've tried it twice since, and both times, my AppleTV's have worked without having to restart iTunes.
I'll keep an eye on it and re-post if anything happens, but it seems that even one wired AppleTV on the network will cause all the others to no longer see iTunes.
Fingers crossed it's that simple! :^)
My guess (hope?) is that when the AppleTV's wake up through the night, they're maybe establishing some sort of connection to iTunes, but the wired ones aren't dropping the connection properly, causing the available connections in iTunes to max out. That's my theory anyway!!