I had this problem after my iMAC 27" 2010 was updated to ML. My Apple TVs 3rd Gen would see the home sharing iTunes library for a while, but if the computer was asleep it would NOT see it.
My short term work around has been to go into settings>Computers>Turn Off Home Sharing... and then turning it back on. All of a sudden my Computer "button" on the ATV3 would show my library information from my iTunes/iMAC.
All of a sudden today this measure was not working. So I turned off home sharing and back on on my iTunes/iMAC. Now, I dont even see Music, TV Shows, Movie lists on my ATV3. (Before the error was when I tried to open the TV Shows I would get error "There are no TV shows....") Instead the current error is could not connect to iTunes library.
I am going to try a reboot of the iMac, ATV3, and Home Network to see if that resolves anything. But this is definitely wonky. I am going to also try signing out and back in on the ATV with the Store ID.
Funny enough, My iPhone and iPad can connect and control the ATV3's via the "Remote" app. So that requires home sharing to be working properly on the ATV. So it has to be something with the iTunes library and ML.