My Mac book pro all of a sudden doesn't have the airplay icon and doesn't work with my Apple TV . Why ?

The Airplay icon will not display if the OS is unable to locate any Airplay devices.

I would check that both devices are connected to the same network and maybe even power cycle the network devices - eg router etc

Maybe even try to connect both devices to another network like an iPhone personal Hotspot and see if that helps to isolate the problem