As long as head is moving it is not the power supply.
First you should print with host and watch temperature graph and heater output. The big question is when any why the temperature is decreasing. Control will be still the same so when it gets colder it will try to heat. So from your description you should see target temperature stay high while temp falls and heater still fires.
At that stage 2 things might happen.
1. A fan was enabled cooling more then you can heat. Have seen users having that problem several times if the filament cooling wa salso cooling the extruder.
2. No power to heater element. Some soldering that looses contact, MOSFET turning off from overheating, defect heater element.
If you have a multimeter and access to fet outputs you could measure voltage when it happens. Helps to see on which side of the connector the problem is.