I have used both a belkin and linksys routers. The router is MAYBE 30-40 feet from one Apple TV (and no walls between) and MAYBE 50-60 feet from the other Apple TV with one wall between them. FYI - both Apple TV's show FULL strength when connected. I don't really suffer from a drop out. My issue is that they lock up the bandwidth. FYI - the Roku and 2 chromecasts are the same distance.
Believe me - I have spend hours working with the router/etc to get a solution - the solution is now to leave them unplugged and after I use them, refresh my router. I'm "ok" with that - it's just clearly not the way it should work
I have the exact same problem with my Apple TV. I run a 5GHz N network, hidden SSID, and the router to my Apple TV is barely 20ft. My Apple TV will just drop out from the network, but then connect again, but it trips up my AirPlay streaming.
I've tried changing wireless channels, but none of my nearby neighbours are running 5GHz networks.
I have a spare AirPort Express, so I may try plugging the Apple TV into that and see how I get on.