I set an appointment at local Apple store Genius bar. The tech helped walk through and eliminate possible variables until we agreed it must be a problem with my router. BTW, the tech hooked up my Apple TV at the store and it worked perfectly using the Apple store network. I went home and restored my router to the factory default (like out of the box when it was new) and re-set it up. When I finished my Apple TV has been displaying the AirPlay icon flawlessly. Hopeful it will continue, but resetting one's router to factory defaults may fix your problem if you are expeiencing same issue when the AirPlay icon goes missing.