Q&A

I would have the battery charged and tested, both a high rate discharge test and hydrometer test if possible. Next I would have the battery negative cable disconnected and an amp meter put in series to check for any parasitic draw on the battery. A long shot but does your car have ABS (anti-lock brakes) it is around that time Subaru had a problem with ABS electrical relay, it used to stick but you hear the ABS motor in the passenger front of the engine compartment running all the time, moisture may aggravate the problem more. There is a Service Bulletin from Subaru about an up graded relay. Finally perhaps moisture is providing a short allowing some circuit to go to ground draining the battery.

When its not raining, with your car running, take a squirt bottle with water in it and spray it around your engine focusing on the ignition system. You're probably going to find that when you squirt a certain part of the ignition system it will die like usual. Repair or replace the part and it should be problem solved.