Might be the battery, might be a bad alternator or misadjusted regulator. Best to do some troubleshooting of the charging system first.
A low battery means a low flap motor RPM, and that means a higher current draw due to reduced inductive reactance in the motor. That shouldn't pop the breaker so easily, but I bet that breaker is old, meaning its contacts are oxidized and have resistance, and that resistance adds to the heating of the thermal strip in the breaker that pops it.
Maintenance is often far behind, and incorrect to boot. From the Comanche service manual:
So when was the flap transmission apart, cleaned and relubed last? Did it get the right lube? Are all the system pulleys turning freely, or are they frozen up as most old pulleys are if they're not inspected?
Using grease or oil on the flap tracks attracts dust and grit and leads to wear and binding. The specified lube might be a dry silicone or graphite lube that stays clean.
Piper wanted that transmission opened and lubed annually or every 500 hours, whichever came first. Annually is a bit of overkill, I think, but I'd bet that most haven't been out in 25 years or more. I know of a twin Comanche that had a gear-up landing because the gear transmission seized up from lack of maintenance.