I cannot find any info on the given model number and probably will not be able to as it is a Haier.

I am thinking that the Thermostat is manfunctioning (just on and off) no in between.
It could be the thermostat.
I am not sure you understand how it works so will try to explain.
The thermostat is just on or off, there is no "in between".
It is basically a switch that opens when the temperature in the unit reaches the set point, shutting off the compressor.
When the temperature in the unit rises the thermostat/switch closes and turns the compressor on again.

Since your compressor seems to be running all the time except during defrost odds are very high that the contacts in the thermostat are never opening.