Run fan continuous

without knowing age of unit, I suggest replacing the motor. Sounds like the armature is worn the bearings and is moving inside the windings of the motor. I would do that first before moving forward with any other repairs.

If fan is temperature controlled, then yes, it should cut on and off with compressor

electric fans start to operate when the coolant temp reaches around 88 c and will run continuously while the coolant is above that temp
if you have ac then there is a fan that cools the condenser in front of the radiator and that will cycle according to the ac compressor cycles

That depends on the manufacturer and in what mode you are operating it. If it's Continuous Mode. Yes, the fan will continue to run, as it's recirculating the air, in an effort to determine if and when the humidity level rises. Then the compressor will turn ON to extract the humidity.

Also, most units will do this if they are running thru the Defrost Cycle. This happens when the cooling coils frost over. It to, is a normal cycle.

So, if you are operating the dehumidifier in Continuous Mode, it's acceptable.
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Hope this helped you. Please let me know. Thanks.

You need to check the contactor. It sounds like the contacts may be getting close to the end of their usefulness and they are welding themselves closed. Check that and let me know what you find.

First, intermittent problems are the worst! I would look for a bad or loose connection. Does the fan ever run consistently? If you turn on A/C most cars will run fans continuously, if yours works ok on this setting then problem is isolated to temp control (fans ok, wiring ok, relay ok) The temp switch would be probably be faulty (or connections). If your fans cycle even on A/C setting then you are looking at a complete electrical inspection. Switches, wiring, fuses, connections, relays, fans...everything! Hope this helps and good luck!

Freezer defrosted everything fan continues to run but will not freeze. Compressor is cycling enough to keep refigerator section cold. 106 Series Kenmore. Turned up thermostat to keep fridge cold and a shorter intermittent compressor cycle run

Replace the water valve.
Problem solved.

Your fan time delay relay has failed.
Replace it.

It's possible that the fan control relay is intermittently sticking causing the fans to run continuously. This can overheat and subsequently blow the fuse. Try replacing the relay and see if anything changes.

Hope this helps.