When I switch to another app on my phone, and switch back to Zwift, I find that the Bluetooth connections need to re-established. For example if I am doing a workout, and switch over to Netflix, then my trainer disconnects.
Trainerroad works perfectly in this mode, so I know it is possible.
Yes experienced same issue of all bt devices disconnected when I tried to go out of app to play YouTube or music etc. Had to re establish the connection.