This was the message after the appeal: "We still found the app is inappropriately using background audio because it is recording audio in the background for an indefinite period of time, which is not appropriate."

Maybe they don't think it's necessary or appropriate to what you're doing with the sound?

Maybe marpalmin was recording and storing big audio files, which might be a privacy issue I assume (if the user forgets the app is running in the background and ends up recording sensitive/private info).

On the other hand I assume that you don't need to keep long audio samples to run your alarm-recognition algorithm and just discard the audio almost right away.

That's just a wild guess of course, it would just seem reasonable to me if the Apple reviewers saw it that way.

I'm not storing audio. Just audio analysis, of course I have a small buffer but that's normal for realtime audio anaylsis. I'm using it to detect footsteps.

Likely that the use case for this app includes it being plugged in/charging.

Well at least is not the idea to use it being plugged. In fact I even added code so that the app leaves background after 1 hr if it did not go to the foreground in between.

I also found other people with the app being rejected for the same reason after asking about it in the apple dev forum.

Maybe they want you to use the motion sensor for that.