I realize that this is a fairly specific resolution, but you could try similar things depending on your system and OS.
Sharing system (important bits):
Windows 7/8 PC
Latest itunes 11.0.1.12
atheros wireless interface
intel gigabit ethernet interface
Problem:
Apple TV 3 starts homesharing fine but then flops out after a run of about ten minutes. You may think that it lasts for longer , even as much as a full length movie, but in most cases that's because the entirety of the media that you watch is actually buffered before the link conks out. So you can finnish your film and then it doesnt do anything else after that.
Solution:
In both the wireless and hard-line interface settings (in windows 7 or 8 under Device Manager) there are options for power savings. "Allow windows to shut down this device to conserve power" or something along those lines. In the intel card case they are even more specific and more advanced than that. In both cases, wired and wifi, disabling the power saving features solved the problem and made homesharing run like sap in spring.
Again, this might not help for people who are having issues with their router etc., but I noticed some people still experience issues with an airport extreme base station, and that really shouldn't be. In cases like this you might want to try this 🙂 given you're trying to home share with PCs in the loop.