Hello,
I'm having an issue with my water heater and I'm trying to determine the source of the problem. The water heater randomly shuts itself off leaving us with only cold water until we hit the reset button on it. There is no pattern as to when this will occur, it could be a day or a week in between or just a few hours. We have had a plumber here who adjusted the settings and said that was probably the cause, he also determine the elements were fine. He did say that if this continued, it would probably be the thermostat. However, I'm beginning to wonder if this may be an issue for an electrician, could something be shorting the hot water heater out? Any thoughts or suggestions?

An Electrician needs to verify where power is lost(feed to Water Heater, Into and out of thermostat, Thermal disc, don't reset themselves, Element intermiddent?)
A Meter will tell all.
If you place an amprobe and meter at the element connections, and you have voltage but not current, the element is open.
Not a typical Pulmber job, but many may know.

Reset button is for thermal high limit safety switch (not electrical over load) and is part of the upper thermostat circuitry. Unless your water is unusually hot just before it turns everything off, it is defective. Not expensive and easily replaced.

Turn off breaker to water heater. Confirm that power is off at heater with multimeter. Take note of wiring. Replace upper thermostat.

P.S.
Since you are already messing around with the water heater, this would be a good time to flush it out. Connect a hose to the drain at the bottom and open valve until water runs clear. Make your heater last a lot longer.

My bet's on the thermostats. The red reset button is a thermal disconnect. If the plumber checked the setting and the waster isn't boiling then the reset button shouldn't be popping off, Replace the thermostats and see if that doesn't fix your problem. Good luck, Tom