I have examined and applied the points in the support links.
Still no Airplay icon appears underneath the Dock in the running Apps section, swiped to the left most.
I have reported this problem a number of times to bugreport.
Usually, I restart AppleTV, iPad device and then it works. But, now, the Airplay icon just won't show.
All devices have connectivity. AirPlay was last working less than 24hours ago.