Apple MainStage audio output device changes automatically after some time
Solution 1:
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.