when you press the button on the tailgate door to lower the tailgate, does it beep ? if you lower the gate by hand does it feel like its "resisting" or does it feel free of resistance?
if you try the fob or the button in the car to close it, it does not lower?
is this a new purchase for you? has this always happened since you had the car or did this just happen?
if you have replaced the motor and arm and its still doing it -- thats a head scratcher for sure. never seen it work one way and not the other.
there is a "manual" feature on the tailgate, in that it will disconnect the motor so you can manually lift and lower the gate, but that does not seem the issue here.
the gate has a "anti pinch" feature, in that if it feels resistance, it will stop closing and raise backup or it will stop, disconnecting the motor. none of this sounds like it could be your issue though.
any trouble codes at the obd port?