AirPlay icon missing on iPad?

Question

iPhone

Ipad 3, iPhone 4S, Apple TV 3 are available. All devices have the latest versions of official firmware. All connected to the same Wi-Fi network (ZyXEL P-330W EE).
From time to time, the AirPlay icon disappears on mobile devices, and in general, it lives some kind of life of its own, now disappearing, then reappearing. If you pause and then resume while watching a movie on your iPad, the stream on your Apple TV disappears. Sometimes restarting the iPad and Apple TV helps, sometimes not.
If you experienced something similar, what helped you solve the problem?

Answer 1

Do not sin on the router? It hurts that you have an old one, and wifi g with its maximum 54 megabits is somehow not the best option for something streaming IMHO.
Maybe something good wifi n, yes 5 GHz (and with simultaneous operation in both 2.4 and 5), yes with MIMO.
If cheaper, then something like:
market.yandex.ru/model.xml?modelid=3659334&hid=723087
If more expensive (but trouble-free with apples):
market.yandex.ru/model-spec.xml?modelid=8291598&hid=723087
Even better:
market.yandex.ru/model.xml?modelid=5045611&hid=723087

Answer 2

The AppleTV is really bad with some WiFi routers. The symptoms are exactly the same, you can make the device reappear on the network either by running through the settings (it helps unstable), or by overloading it.
I was helped by connecting it with a wire. Everything began to work like clockwork.