I realize this is a old post but I got a fix to anyone experiencing frequent disconnects between AppleTV and another device on your network..
Whichever device that has iTunes and has the music/movies stored on it, make sure the firewall on both Windows and your antivirus are disabled.
Go into your router settings and port forward TCP 3689 , UDP 5353. Your forwarding ports on the device that has iTunes on it, not the AppleTV.
Worked for me.. no more issues after that.