Question: I am living in my travel trailer full time. Should I turn off the hot water heater between uses or let it run? What uses more propane in the long run?
Answer: It will really depend on several factors. One would be the efficiency of your water heating system. Another is how often you use the hot water and are turning it off and on.
If you are going to be fulltiming for a while, your best bet might be to do a couple trial runs to see which uses more propane over a period of time. That way you will get the real answer for your specific setup.
Another consideration if you are have a hookup with unlimited electricity most of the time, would be to install a small electric hot water heater that will meet most of your needs. You would have to weigh the cost of buying and installing the electric hot water heater compared to any potential savings.
By the way, some propane hot water heaters also have an option to run them on electricity.