There are a couple of possibilities. First and most likely problem is the reset button. Even though it may look and feel OK, something goes bad on the inside of them which allows the voltage to drop off and eventually the shutdown occurs. So, I'd try that first. Second, the wires going to and coming from the reset should be replaced if the ends are discolored, especially if they are black or close to being black. Here again, corrosion can occur between the female connector and the male end which slowly cuts down the voltage and pop, off it goes. So, the wires are available or you can make your own, if you have that capability, just use at least #14 stranded wire, with a good quality connector. If that doesn't work then try a new heater.
The Amazing Morandini, March 2014