Your altenator charges the battery continously, as long as your car is running. When in Accessory / Accessory II, your car runs off the battery, nothing is charging it. So if you are listening to it with the car off then your battery will die relatively quick depending on how much power your system is "drawing" from the battery.
That's what he meant by "too much draw".

BUT if the battery died while the car was ON then that means you probably need a heavier duty altenator to charge the battery at a faster rate.

Edit:

I should learn to read friggin' replies before I hit reply. :/ Guess you've already been helped.

Maybe tonight we'll fly so far away... We'll be lost before the dawn...