Shutting the tailgate by hand should not cause any damage to the motor, although of course this is less than ideal. There are a number of potential causes of the fault - the fact that it will still open correctly suggests that the motor itself is fine, although any excessive resistance when closing would cause it to stop as it could falsely detect this as an obstruction. Faulty sensors or damaged wiring or fuses could prevent it from operating correctly, and some owners have reported that water ingress around the rear wiper has caused the problem, but to get to the bottom of the issue will likely require a close inspection. You can perform a reset of the system by opening the tailgate manually then holding down the button for 10 seconds until the lights flash, and you may wish to look behind the rear panel for signs of water damage. Alternatively we would suggest having it checked by an independent Audi/VW specialist near you.