Since we are basically living in our trailer at home (driveway full timing), I've been keeping the water heater on gas (6 gallon), and the cover on the inside of the camper is currently removed, since I have not put it back on after un-winterizing. With the cover off, I can hear the gas burner kick on and off, and we're inside the camper a lot! It seems to kick on after running hot water from any faucet, but only very, very rarely do I hear it kick on any other time. It uses very little propane. If the water heater is the only thing using gas, and you never ran any hot water from the faucets and you just let ambient temperature cool the water heater, and let it heat naturally that way.... a 30 pound propane tank would keep the water hot for probably 8 months.
How much propane gets used, depends upon how much water you use and the ambient temperature around the water heater. Of course, the colder it is outside, the harder the water heater has to work. And the colder the water is coming IN TO the tank, means the water heater has to work harder to raise the temperature. It takes more propane to heat 40 degree temperature water to 130 degrees, than it does if the water is already starting out at 80 degrees when entering the tank. So, really, there are a lot of variables which will determine how much propane actually gets used.