I have to turn my Apple TV on to make it discoverable by laptops/phones
In my experience, the "sleep after X" is the solution. If I can't see on my apple tv the power diode on - the device is at sleep and I will not be able to use it as a target for airplay. 

It should be said my apple tv is only connected through wifi. I wonder if connecting it through ethernet would make any difference (although I suspect it wouldn't).