Try clearly specifying the user visible features of your app that require and use persistant background audio recording. You can put this information in the Notes section of App Review Infomation in your iTC submission. You might also want to make sure that those features are clearly described in the app's documentation and the App store description so that the user knows about them as well.
If your app is useful without persistant background recording, you might want to add a switch somewhere, so that the user can turn background recording capability off, and document this as well.
Same problem here... An update for my app that always used the background audio key to record audio while in background just got rejected.
The app analyses audio while in background in order to sync Philips Hue lights to music, and I cannot ask all users to set the auto-lock timeout to never.
I just made an appeal to their decision, but I'm not sure they are going to change their decision.
There is an inconsistency between the documentation for the background audio key, and the review guidelines:
UIBackgroundMode audio - The app plays audible content to the user or records audio while in the background.
Multitasking apps may only use background services for their intended purposes: VoIP, audio playback, location, task completion, local notifications, etc.
Did you manage to get your app approved in the end ?