AirPlay icon does not appear in iPaid control center.

I have a recurring problem when I try to use AirPlay and my Apple TV. The icon sometimes appears within the control center on the iPad and sometimes nothing shows. I have checked network connections, rebooted both the iPad and the Apple TV, even checked my modem settings. The iPad is connecting to the Internet through my wireless network. So does the Apple TV. There does not appear to be a pattern for this. So far I am baffled as to why this happens and would appreciate some advice as to where else to look.