I'm having a problem with a digital t-stat

Digital Thermostats... good idea on paper, but in practical use they are less than desired. Get an inexpensive mechanical thermostat, wire it in, and run the unit. When you reach your comfort zone adjust the temperature on the unit so it just shuts off, and LEAVE IT ALONE.

heating and cooling are more than just making the air the right temperature, EVERYTHING in the space needs to reach the desired temperature, walls floor, furnishings....everything. And while it is true that a digital thermostat can save you a few cents per hour in operating costs, the time you spend to learn how a particular high tech device works, experimenting with the programming, possibly battery back-up power to maintain a program, the hassle is just not worth the savings, particularly in an RV where you spend limited time anyway.

wiring a standard thermostat is green for fan control, red for power in, white for heat, and yellow for cool. You can test your unit's function by connecting red green and white wires to check for heat, red green and yellow wires to check for cool.

If these tests fail, most likely you have a bad component on your control circuit board and it should be replaced. If you have experience with circuit diagnosis and repair you could save a buck by replacing the bad part of the board, but most folks will save time and money simply swapping out the entire board.

If the tests for function pass, then wire in your new, simple, easy to operate $20 thermostat and call it a win.

It may be a wiring problem at the thermostat, quite often there is a jumper missing in the thermostat between the R terminal and the RC terminal. hope this helps