I've found that, with my water heater, the propane pilot light usually keeps the tank hot - at least in the warmer summer months. On the other hand, if I'm hooked to shore power I run it on electric. It goes on when we're stopped and off when we're travelling.
2003 GMC 3500 D/A, CC, LB, 4x4 and 2000 Airstream Excella 30. WBCCI 7074