this is a mute issue, if your buying a converter/charger to keep the battery's charged, then the stereo will play just fine since the converter will keep up with the stereo usage,
if your twin 6v(12v) batteries are in good condition. then you have a problem with the stereo, either not getting enough voltage due to wiring issues, or if cranking it too high and loud, the amp inside the deck can potentially be overheating and shutting off to protect itself
i ran 8 speakers and 2 subs, around 1000w rms, off a single red top 12v battery for over an hour before issues.
hooked up to a 20 battery charger it will play for days
no need to bounce between battery's