From a themodynamic point of view, it uses more energy to keep the water hot all the time than to turn the heater on and reheat as needed. This is also true for the furnace for the air inside the RV, for that matter.
This fact is a little clearer if you approach it from the point of view of energy leaving the system (the water heater) which, absent water use, is basically just water radiated to the environment through the tank etc. Since the heat transfer is proportional to the difference in temperature between the water and the outside, the heat is lost fastest when the water is hottest. Keeping the water at a high temperature constantly means more energy is radiated away, and that needs to come from some fuel--propane, in this case, or possibly electricity.
There are a few odd cases where it turns out that maintaining temperature is more efficient because the efficiency of the heating system is quite variable. One example (not likely for an RV) is with many geothermal heat pump systems where attempting to extract a lot of heat at one time from the ground depletes the supply (cools down the ground loop) and lowers the system efficiency considerably. A constant, lower level of heat transfer is much preferred to a sudden burst, and maintaining temperature is more economical than letting it cool and trying to bring it back up. Propane flames and electric elements do not act this way, of course.