I have been battling this issue for months now too. Last night I fixed it, finally. My problem was in how I had Home Sharing turned on. I didn't. I had Sharing turned on, in the Preferences>Sharing tab, and that enabled my Apple TV to see and play my TV Shows, Movies, and Music. But, like most of you here, it would disconnect all the time. It always bothered me that it wasn't labeled Home Sharing, but rather, just Sharing.
Last night I read another post that mentioned going to the iTunes File menu to turn Home Sharing off and then back on. So I went there and mine was NOT turned on! Yet Home Sharing WAS working, albeit with the frequent disconnects that were driving me crazy.
So I turned Home Sharing on from the File menu and it has been rock solid since. I'm sure many of you already have yours turned on there, but for the rest of you, check and make sure. Because like I said, just having it turned on in the Sharing tab of Preferences will work, but with many disconnects.
Hope this helps some of you. I feel pretty stupid for not checking this earlier.