To bad you don't have a scope. But the symptom suggests that the HPWM pin is going high, or at least to a very high duty cycle. It should go to zero volts(gnd). If the HPWM command is not playing nice, then you might try using the MIN operator to limit the ADC value to 1.

As far as as pull down resistor goes, a 47K resistor going from GND directly to the gate of the MOSFET base will keep the FET off in case for some reason the HPWM pin floats. 47K will also prevent glitching when the device is powered up. It will not affect the gave drive voltage or the LED. This is pretty much standard practice. I assume you are using a logic level FET?

Are you sure that the value is at zero when this happens and that the duty VAR is not somehow overflowing to 255? . A simple test would be a bare minimum program that simply does something like below. It should be on 2 sec then off 2 sec.
Code:
' Defines here  

DO

        HPWM 1, 0,1000. 
        PAUSE 2000
        HPWM 1,255,1000
        PAUSE 2000

LOOP
A schematic diagram and a posting of your code would be helpful.