Okay To Leave Batteries Connected While Stored?

I can only speak for my system. I have only one 12v battery, original and 5 years old. I always leave mine in the trailer and trailer plugged in year round. Only thing I ever do is check the water once a month and keep the connections clean. Unplugged, mine will drain it in about three days from gas detector and parasitic losses. If you can plug it in and are sure no one will mess with it, I'd let it plugged.