Ok , I have come to a conclusion concerning the dead battery syndrom. First it appears that if I leave my Stang sit for over a week, the battery will be dead. Second, it appears that a slight loss in voltage during that week of sitting, will send my Shaker 500 into a frenzy of CD changes all by itself. Third, if I don't notice the Shaker doing it's thing (ie I walk near the car at some point and hear the thing going nuts) it will drain the battery down to nothing. So I surmize that over the week of letting the car sit, the normal voltage drain can be enough to allow the battery voltage to drop below a critical voltage for the Shaker( what this minimum voltage is I have not yet determined). This loss in voltage entices the Shaker to initilize itself over and over and over until the battery is drained. In summary the Shaker may well be the reason Mustangs have an exceptional amount of battery failures.
I seem to remember a post about this a few months back. I also believe someone had posted that there was a recall of sorts on the Shaker system, but i don't remember the specs on the whole ordeal. You may want to check into it, because yours definately seems to have a mind of its own. I left my car for 5 days, the battery was dead and needed buried. Went to get a new battery and the mechanic guy said that according to their computer system, the original battery was really too small to crank the car. They installed a larger one, one rated for a Shelby. Never had a problem since. The original also was small in size and had a blanket around it. The mechanic said to ditch the blanket because they actually will harm the battery(something to do with retaining heat damages the battery?), and the new battery takes up the entire designated space. Now, I can leave the car for 5 days, and it still fires right up.
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Some observations DEAD Battery - 
