Unless you are using it, you will likely want to turn it off, because when not operating, inverters can and do draw some current from the batteries. If you have a remote display/switch and if you plan on not using the inverter at all for a while, you should turn the inverter off with the actual switch on the inverter, otherwise the inverter will still draw some power, not as much, but some to charge the capacitors. Leaving the inverter on all the time will not hurt it, it will just draw down battery power which you should be aware of. Also if you are using shore or generator power, you will likely want to turn it off.