Make sure it's not set to stop when it's not the foreground app. If you can't change that, use a different radio app - one that can play in the background.
I use drivemode instead of Android auto. Music will play while navigating. I don't have Bluetooth built in to my car. So I bought a Bluetooth to aux adapter and it works pretty well. Just have to turn down the volume before I turn off my car. Otherwise I'll get blown away by the radio when I start my car because the radio is the default source over the aux input.