FWIW, I remove my battery while the car is stored over the winter and keep it in the basement sitting on a piece of wood. I put the charger on it about once per month until it reads 100% and then remove it. I also don't feel comfortable about leaving this sort of electrical thing going unattended in my home for extended periods of time.
I also didn't know there was supposed to be a rubber mat under the battery. My car doesn't have one of those, but it soon will!