If the freezer is not getting cold enough to satisfy the thermostat setting it will not shut off. You did not state what the temperature inside the freezer is or what number the thermostat/cold control is set at. Will it cycle off if you were to turn the cold control to a warmer setting? If the will not shut off when you turn the cold control to the warmest setting it could have a stuck contact in the cold control.
If there is no visible frost on the lower panel inside the freezer that would basically eliminate any defrost failures. It could have an inefficient compressor or the unit could be short on Freon too causing the cut off temperature to not be met and causing it to run all the time. It must be shutting off at some point in time because it does have to shut off and start the automatic defrost cycle since it is a self defrosting freezer.
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