When the car's shut down the 12V battery powers the alarm system (which can't be disarmed or shut off), the cabin lights, the door locks, and the back hatch. Shutting down the car also shuts off the things we might forget, like headlights. If you shut down the car you can't even use the power windows.Since I don't have a Prius, I don't really know... but wouldn't there be a lot more intermittent and constant loads on the 12V aux battery than you mentioned?
Like lights, both inside and outside including brake lights, and power windows, cabin HVAC fan, door locks (like a hatch release ), ABS pump, electric fuel pump (usually a big draw) for the fuel injection, etc?
Once the car boots up, though, all the electrical loads are powered by the main battery through the motor generator or the inverter. And of course the internal-combustion engine comes on from time to time to help recharge the main battery.
I'm being told on PriusChat that the Prius 12V battery-charging system is pretty rudimentary (just a constant voltage) and slow. So I might've discharged it through a combination of short trips and leaving the back hatch open. But no problems since, and this morning I gave it a solid 60-minute round trip to White Plains Beach. As long as the surf is good then I shouldn't have this problem...