I had 4 AppleTVs (3 connected to network via Ethernet, 1 via wifi) and a mac mini running iTunes (connected via Ethernet) with an AppleScript running every 30 minutes to count the number of zombie connections and restart iTunes if necessary. Result: iTunes had to be restarted every 2-3 hours, day or night.
I broke down and decided to change my 3 ethernet AppleTVs to wifi which I didn't want to do because I didn't want to saturate wifi or impact other devices trying to use the network. However, it did solve the home sharing/zombie tcp connection issue very quickly. It has been 3 days now without a single iTunes restart.
2012-09-12 02:32:26 Restarting iTunes now
2012-09-12 03:02:05 Found 0 0 27 0 4 AppleTV connections!
2012-09-12 03:32:05 Found 0 0 54 0 4 AppleTV connections!
2012-09-12 04:02:05 Found 0 0 81 0 4 AppleTV connections!
2012-09-12 04:32:06 Found 0 0 105 0 4 AppleTV connections!
2012-09-12 04:32:27 Restarting iTunes now
2012-09-12 05:02:05 Found 0 27 0 27 4 AppleTV connections!
2012-09-12 05:32:05 Found 0 57 0 57 4 AppleTV connections!
2012-09-12 06:02:05 Found 0 84 0 84 4 AppleTV connections!
2012-09-12 06:32:05 Found 0 107 0 107 4 AppleTV connections!
2012-09-12 06:32:26 Restarting iTunes now
2012-09-12 07:02:05 Found 0 0 24 0 4 AppleTV connections!
2012-09-12 07:32:05 Found 0 0 42 0 4 AppleTV connections!
2012-09-12 08:02:05 Found 0 0 60 0 4 AppleTV connections!
2012-09-12 08:32:05 Found 0 0 78 0 4 AppleTV connections!
2012-09-12 09:02:06 Found 0 0 96 0 4 AppleTV connections!
2012-09-12 09:32:05 Found 0 0 109 0 4 AppleTV connections!
2012-09-12 09:32:27 Restarting iTunes now
2012-09-12 10:02:05 Found 0 15 0 15 21 AppleTV connections!
--------THIS IS WHEN I SWITCHED APPLE TVS FROM ETH TO WIFI---------------------------
2012-09-12 10:32:05 Found 0 0 3 0 9 AppleTV connections!
2012-09-12 11:02:05 Found 0 0 3 0 11 AppleTV connections!
2012-09-12 11:32:05 Found 0 0 3 0 18 AppleTV connections!
2012-09-12 12:02:05 Found 0 0 3 0 9 AppleTV connections!
2012-09-12 12:32:05 Found 0 0 3 0 10 AppleTV connections!
2012-09-12 13:02:04 Found 0 0 3 0 6 AppleTV connections!
2012-09-12 13:32:05 Found 0 0 3 0 6 AppleTV connections!
2012-09-12 14:02:05 Found 0 0 3 0 15 AppleTV connections!
2012-09-12 14:32:05 Found 0 0 3 0 11 AppleTV connections!
2012-09-12 15:02:05 Found 0 0 3 0 13 AppleTV connections!
2012-09-12 15:32:04 Found 0 0 3 0 9 AppleTV connections!
2012-09-12 16:02:04 Found 0 0 3 0 8 AppleTV connections!
2012-09-12 16:32:04 Found 0 0 3 0 9 AppleTV connections!
2012-09-12 17:02:05 Found 0 0 3 0 4 AppleTV connections!
2012-09-12 17:32:04 Found 0 0 3 0 4 AppleTV connections!
2012-09-12 18:02:04 Found 0 0 3 0 4 AppleTV connections!
2012-09-12 18:32:04 Found 0 0 3 0 4 AppleTV connections!
2012-09-12 19:02:04 Found 0 0 3 0 4 AppleTV connections!
2012-09-12 19:32:04 Found 0 0 3 0 4 AppleTV connections!
2012-09-12 20:02:04 Found 0 0 3 0 4 AppleTV connections!
2012-09-12 20:32:04 Found 0 0 5 0 4 AppleTV connections!
2012-09-12 21:02:04 Found 0 0 3 0 4 AppleTV connections!
2012-09-12 21:32:04 Found 0 0 3 0 4 AppleTV connections!
2012-09-12 22:02:04 Found 0 0 3 0 4 AppleTV connections!
2012-09-12 22:32:04 Found 0 0 3 0 5 AppleTV connections!