I have a Mitsubishi Electric “MSZ-GL06NA” and live in NYC.
Why does the heat pump never stop when set to the dehumidify mode?
The apartment just keeps getting colder and colder but never any drier(?).
When will it ever stop or Does it need servicing?
Sounds like either a) the dehumidifier is broken or confused b) your apartment has more moisture in it than you thought or c) the moisture is being replenished from somewhere.
I stayed in a friends house a few months ago and she had 4 dehumidifiers running since she bought it. The house was built before damp proofing was a thing and set into a hill, so the place is basically one massive wick for groundwater. It will never be over for her.