I have a 987.2 Boxster, so the same issues owned for over 10 years and one battery replaced. These cars are indeed battery sensitive as soundly advised above.
My 987.2 will 'go to sleep' in 7 days from fully charged, and will be very weak by 2 weeks and then thereafter it is a heap of trouble to get to open the car and sort the battery, I have done this once, you do not want to do it a second time.
I do not connect to a conditioner as the car lives outside all year, so a different approach by me. I usually attach a charger to the car for a few hours every week or so esp in the winter.
I personally would change the battery for new so you know where you are. This will reset a few controls, but are simple to re-establish or take it to a good retailer of batteries and let them get it straight.
For the cost, not worth the worry.