You don’t need the TV to be ‘on’ to play Airplay audio to the Beam whilst watching the video on your mobile/tablet device - if trying to cast the video aswell to the TV however, then that’s likely going to be a TV issue, or mobile device issue, rather than a Sonos issue.
You might want to first try powering off (not standby) all your devices including your local router for a couple of minutes and bring them all back online to see if that fixes your issue. If not, then you perhaps need to detail the steps you’re taking to play the A/V source so that some further suggestions can be made.
You cannot use Airplay to send a video signal to the Beam: its an audio-only device. you can only send it audio.
Thanks for the replay merry xmas