A refrigerator keeps running until its internal temperature matches the desired temperature coolant setting. The primary problem that keeps a refrigerator running longer than usual is either a blockage in airflow between the freezer and refrigerator or a lack of refrigerant.
The first troubleshooting step involves looking at the top of a frost-free refrigerator. If frost is forming, this means that the thermostat is not calibrated correctly or is faulty in some other way, but the refrigerator has enough refrigerant.
Even if no frost is present, the cold control can still be the problem. If the motor keeps running even when the cold control is set on the warmest setting, the control itself is broken. At this point, a repair call is necessary, and it is recommended to have the repair representative check the defrost timer and heaters on the same service call.
If the motor responds to the changes in the cold control but keeps running when the cold control is in the desired position, it's time to look at the condenser coil, either on the back or at the bottom of the refrigerator, behind the kick plate. Dirty coils keep the refrigerator from working efficiently, and regular cleaning is recommended by most manufacturers. Another step is to check the drain line beneath the evaporator coils. Water should be dripping into this pan when defrosting is taking place, and if this pan is dry, there is a blockage somewhere that could influence the cold control.