for me it gets worse, ATV3 issues originally started with Home Sharing drops, then progressed to WiFi drops (on an Airport Extreme at 5Ghz).
I did a reset of the ATV, sometimes the device reconnects, other times it's stuck on the main screen with only a 'Computers' and 'Settings' icon. Performed a full restore in iTunes, everything came back and worked for about 5 minutes before dropping Home Sharing. Upon investigation it was all of WiFi down again (no podcast, no Netflix, etc.)
Switched the Airport Extreme to 2.4GHz, same results. Turned off the Airport and went with the ISP supplied router, same results. Makes me think the WiFi module went bad in the ATV3 except it was flawless for 4 months. This didn't happen until the same day I upgraded the computers to 10.8. Coincidentally, I am having issues on the MacBooks with holding a 5GHz connection as well. Then you might suspect the Airport Express is flaking out (2 years old) but the ATV3 exhibits the same issues on the ISP wifi router at 2.4GHz so it's an endless cycle at this point that didn't exist the day before 10.8 came out.