Some things I would suggest:
1) How old is your battery? It could be that your battery is simply old and no longer holding a charge. You can usually take it into an auto parts store and have it tested. This is the easiest thing to test and easiest to fix.
Battery is new - I bought another battery thinking my old battery was bad - this one has the same issue. I had the new one tested as well since I thought it was bad. They said my alternator and battery tested okay.
2) Have your Alternator checked. If it is no longer functioning properly, it may not be able to meet your needs and recharge the battery.
It was replaced a year ago, and was tested by Interstate as okay - was pushing 14.5V to the battery when my car was on.
3) What is your commute like? If it is short, your alternator may not have enough time to recharge the battery after starting. If the battery and/or Alternator are bad, that will compound the issue.
Varies. Roughly 15-40 minutes depending on traffic or going to work or school. After my battery being dead this afternoon (around 3pm), and driving around doing some errands, my battery was at 12.5 volts after sitting for a few hours - Mac Mini shut off.
3) As TeamRSX suggested, put an ammeter on the line from the battery to the P1900. That will tell you if there is a draw that there shouldn't be (possibly a short which could actually damage both your battery and alternator).
I couldn't get my ammeter to work - any tips on using it? It's just a basic Radioshack Voltmeter combo.. I thought I'd be able to put the positive/negative leads on the battery terminals and measure it. It came out as zero which can't be right.
4) Figure out what your draw is, it could be that your Alternator is fine but just under powered for your needs.
Will need to figure this one out...