Water Heaters - Electric Water Heater problem

I have a 42 gallon electric water heater which should be plenty for my very small, single resident home. What happens is I can run the hot water for a bath or to do dishes and the water is very hot. I have lowered the setting to below 120 degrees but the water still seems hotter than that. Very quickly, not even enough to fill the bath with warm water the water goes cold and I have to press the red reset button on the tank to get any more hot water.

Can someone tell me what it is going on with it and what I am going to need to replace?

I have had this very same problem. Either you have set your water temp too high causing your thermostat to trip or you have a faulty thermostat. You can get a new thermostat at any hardware store. Make sure you shut off the electrical power to the water softener before doing any work.
Another possibility is a huge build up of lime and sediment on your heating elements and on the bottom of your water heater tank.

I'd flush the tank anyway if you haven't in a while. Typically, hot water but only for a short time is a lower element problem.

I hadn't really considered flushing the tank but I did forget to mention that the tank is less than a month old.

Who installed it? Surely it's under warranty.

Yeah, less than a month old does seem to be an important piece of information.

Was your hot and cold piped backwards on the tank?