Hi G&E,
The tank heaters won't burn up if left on. Theoretically, you can leave them on indefinitely. Some people accidentally do. Your 2005 model does have only one battery so you will need to be watchful of draining your battery when the heaters are left on overnight. One or two batteries, it is ideal to be plugged into shore power when the tank heaters are on and you are parked for the night. Tank heaters can be kept on all the time during the day if driving your motor home during the day for your chassis engine alternator will maintain your house battery properly.
Ron Dittmer