Visually determine whether the compressor is turning with the EC lamp off. If so, you could have a heater fault or very low refrigerant (but still enough to start the compressor). If not, and the pushbutton unit doesn't notice, I have no clue what could be wrong. Perhaps it's a bad pushbutton unit.

Note that it is not normal for your compressor to cycle on this model. The only reason that the compressor should ever shut off is the evaporator getting below 37F. The compressor does not cycle off if cooling is not demanded; rather the heater starts up.