Apple MainStage audio output device changes automatically after some time
After some frequent contact with Rogue Amoeba we came to the following solution.
Strictly speaking is this not an answer to the original question, but a workaround.
I used the Loopback device to connect to Audio Hijack, but another solution is to select System Setting as Audio Output in MainStage. Then I captured the MainStage application in Audio Hijack instead of the Loopback device. Thus circumventing to whole need for Loopback as an input device into Audio Hijack.
BTW I still use Loopback to connect the Audio Hijack output further in the chain.