Can you make this happen? If so, watch the compressor/fan contactor when the inside unit shuts off and see if the contactor is disengaging. If not, then check contactor coil voltage. If no voltage when this happens then replace the contactor. The icing up may be from the compressor continuing to run without the blower running to keep the unit from freezing up. Does the blower fan turn off before t-stat temp is reached? If so the problem could be with the air handler and not the compressor.
You'll have to run the system and check the symptoms to isolate the problem.