Hi all: I had this issue and it resolved when I tweaked my router settings. So I figured I'd pass it along, maybe it'll be helpful to you. My issue was that when I was streaming media from my computer to my Apple TV, it would drop the connection. I have strictly wireless netwok, aside from my TV which is hard-wired into my router.
I can't speak for everyone's issue but a few things I've noticed with most of the people: 1) Having dropped connections via an Apple TV to a computer streaming media 2) Connection is strictly through wireless only (no hardwire connections via Ethernet)
Unfortunately, given this information for all of those demanding an answer from Apple, your requests are going to fall on deaf ears, because this is a router/home network issue, not a software or hardware issue. So any effort in reinstalling or re-configuring your network may not help. In my experience, Apple TV drops the connection if there is ANY slowdown in the transmission rate. Meaning while most streaming services (ie. Netflixs) may just decrease the quality of the media, Apple TV does not.
To fix this issue, you need to configure your multicast rate in your router settings to high. Unfortuntely, if you have a large area network, you may lose some of your connections of your wireless clients the further you are away from your base station router or they are unable to handle the increased transmission rate. Basically, having an increased multicast rate setting on your router means that the router will only accept connections from wireless clients in range AND have the ability achieve high transmission speeds. If you have this issue, than you may benefit from increasing your transmitter power or installing a WDS relay.
If you have a Apple router the multicast rate configured under the Airport Utility -> Manual Setup -> Wireless (tab) -> Wireless Network Options -> Multicast rate
I would suggest if you are still having this issue, than you need to get a router that has at least a gigabit transfer rate such as 802.11 b/g/n. A slow processor might cause this issue as well.
Hope this helps!