Have you try to connect apple tv directly to HDMI A on the stage instead, make thats any different?
But it also strange it drop out of sound in the apps on the TV also.
Of course you have reset your stage to factory would i think, and the tv :) But if not try that also.
If nothing of this work, i would recommend you to send log fil to B&O true the B&O app, and explain your setup and what you have trie, and the drop out is not in music source, only with video source true the LG tv and HDMI source. So B&O can analyse it. give them also information of time and date and source its drop out before you send the logfil. Time and date is important they can go directly into the log at the specific time you have the drop out, and see what it can be. :)