This is going to seem like a weird and totally unrelated question, but work with me on this. 🙂
Have you programmed any third-party remotes (like a DVD player's remote) to work with the Apple TV? Or do you only have/use the Apple remote?
I ask because a few months ago some of us were trying to figure outwhy certain users' Apple TVs would not wake for AirPlay requests while others' would. There was no rhyme or reason regarding versions of ATV, serial numbers, etc. I finally decided to experiment and reset all of the settings on one of my ATVs. In that "pristine" state, it would not wake for an AirPlay request when asleep. However, as I started reconfiguring it, I re-checked after each step to see if/when it would work properly again. After programming the ATV to work with my DirecTV remote, bingo, it was waking properly again. I went back and forth and was able to get the same symptoms with and without the remote programmed.
It doesn't have anything to do with the actual use of the remote and from others' tests, it doesn't seem to matter what remote is used. The only thing that I can think of is that when no additional remotes are configured, the ATV knows it doesn't need to listen for RF signals (the Apple remote is IR) and maybe it is inadvertently shutting off the networking along with the IR receiver when it goes to sleep.
Anyway, if you want to experiment and see if that works, report back.