If you are getting cutouts, there are many times voltage protection built into head units and amps. I doubt the stocker has this, but it's possible. If you are running off the cranking battery, there is a good chance that when voltage drops, the head unit or amp will shut down certain channels. It can be random.
Our system is run of a second deep cycle battery. When the tower speakers don't fire up, or the sub doesn't come on, I know that the Alpine voltage protection is keeping them from lighting up. They are on separate amps. Then I know it's time to fire up the engine and go tubing, or be sure to put on the charger once back at the dock.
It's possible.