That sounds frustrating!
I don’t have a Stage but I thought that the RJ45 (rather than hdmi CEC) was used for control of the connected TV. I just had a quick look at the set up instructions, and noticed the following:
2 – Go to the TV’s Connection menu, then find HDMI Device Settings and disable “Auto
Device Detection” to allow Beoremote One to control your HDMI connected device to
Beosound Stage.
If you haven’t done the above, could it be that the TV is ‘auto-detecting’ the lack of Stage hdmi output (when airplaying) and shutting down?
As an aside, whilst living in a rental my TV and Audio are currently not connected by Masterlink or whatever. I find this quite refreshing as it allows me to listen to the standalone radio (original BS1) whilst the TV is on Mute. I am finding it especially useful this week to watch the televised QE2 activities without the BBC commentary!