Turn them off, no reason to leave them on. Memory settings are saved by the batteries or NVRAM.

Also, this is all assuming the batteries are still good and that they haven’t leaked and done any harm to the MPU. Make sure you open the back box and check and if you aren’t certain, replace them with at least some lithium versions and consider moving them to a remote holder or replace with NVRAM.

Turn it off and on as many times as you want. Some people have power cycle panic attacks.

the same way you wouldn't leave your car running when you park it, you wouldn't leave a machine on when you're not playing it.