Exact same problem since a long time. Started after an ITune upgrade 6 months ago if I remember correctly.
Im using Home Sharing. I have IPad,IPhone and 2 Apple TV one 2nd (Wifi) and one 3rd gen. Wifi provided by Apple Express. Home sharing work great on all device without interupting playback and/or disconnecting until I leave iTune server hosting Home Sharing idle for something like 2 hours. I have tried many time to access Home Sharing from any of my Apple device before that said 2 hours idle and it connected properly. Like you, it mostly happen overnight while iTune is idle for a long period. When it happen, all devices stop detecting ITune Home Sharing. Remote Apps and/or Music Home Sharing can't connect. Doing of one of the points down below temporarly fix problem on all devise and they connect right away until everything is idle again.
1) Turning OFF then ON Home sharing temporarely fix the problem (Until next idle).
2) Closing Itune also temporarely fix the problem.
Since long time (Before this problem started) I have ITune installed in a VMware virtual machine running Windows XP SP3 32bit on top of an VMware ESXi 5.0 host. First I though it was more of my unusual setup causing the problem. I have tried a lot of things. Scratch reinstall, removing firewall, removing all kind of power features on host and OS it self.No anti-virus, no other software installed. Running out of idea. Now glad to see some else have the exact same problem.
Will keep looking and post if I find anything.
What is your setup hosting iTune ? PC, Mac + version ?