The water heater has a thermostat that controls the temperature of the water. As long as it is operating properly, there should be no issue leaving it on for extended periods.
You would want to shut it down at intervals and flush any sediment out of it, and restore the air bubble that reduces surge in your water system. (or do what many have done and install a surge tank somewhere in the system.)
The only thing I did not like about the standard AS water heater was its tendency to come on and noisily heat water in the middle of the night. Since our heater is located in the bottom of the wardrobe closet and is right next to the head of our front bed, the noise used to wake me up occasionally. Because we tend to camp out in cold weather, we could not turn it off at night under freezing conditions.
To solve that, reduce the weight forward of the axles, and provide massive amounts of hot water so my wife can enjoy "hotel showers" on the road in the Airstream, we installed a PrecisionTemp 500-series tankless water heater. That unit is essentially silent unless we are actively using hot water, or if it gets below freezing, and it has to protect itself from freezing up.
Not a cheap change, but wife is happy, so it's priceless...it also makes very little noise when heating water, or at least the sound of the shower and sometimes the water pump totally drowns out the sound of the little fan that circulates the air for the burner...
Rich, KE4GNK/AE, Overkill Engineering Dept.
'The Silver HamShack' ('07 International 22FB CCD 75th Anniversary)
Multiple Yaesu Ham Radios inside and many antennae sprouting from roof, ProPride hitch, Prodigy P2 controller.
2012 shortbed CrewMax 4x4 Toyota Tacoma TV with more antennae on it.