I was able to measure the parasitic current drain on my Ascent and I'm happy to report that there does not appear to be a problem. This is good news because if there was a problem here, it would be next to impossible to fix. The Ascent draws only between 15-25ma when powered down, (i.e. no accy, no ignition, doors closed, all lights off). This is well under the 50ma acceptable limit. 15-25ma is not an unreasonable parasitic load on a battery and should not draw down the charge for any reasonable length of time. I could not find the amp-hour rating of the battery so I could not calculate specifically how long it would last with this load, but a battery of the size used in the Ascent is typically around 37 amp-hours. With a parasitic current loss of only 15-25ma, such a battery should last for many weeks before being fully discharged.
That said, the Ascent can still be tough on a battery. As soon as you open the door, the amperage draw goes up to around 4 amps. And since the lights are delayed before they go off after the door is closed, this adds to the drain. Also, when you turn off the ignition, the headlights stay on for a while as well. All of this can add up. I assume the alternator can keep up with the high powered HK amp, the heated seats, the heated mirrors, the rear window defrost, etc., but the battery may not get the best charge when all these high powered accessories are being used.
I used a 500A battery load tester to test the OEM Subaru battery and the results were not great. The battery is rated for 530 CCA, so to test it a 250A load was applied for 15 seconds (the battery was fully charged just before the test). This was repeated three times within 5 minutes. It passed, but just barely. The tester was right on the line between "OK" and "Replace". This is not impressive for a new battery. The battery is manufactured by Johnson Controls. They usually make decent batteries, but Subaru may have specified a cheaper design to save money, who knows.
Considering all of this, I would probably recommend purchasing a better battery if you have issues with the OEM battery going dead or discharging repeatedly. The question is, are better batteries currently available in the size required? I'll dig into that next.