Problems with the flap motors almost always are caused by electrical problems inside the motor unit. If the climate control computer detects any problem it disables the motor to prevent the motor from breaking the flap mechanism. This obviously manifests itself in the flap staying in position, but its not "stuck" in a mechanical sense, just switched off. When a motor is disabled, this is reset when the power is turned off.
The most common reason for this is wear in the position sensing potentiometer. The temperature flap is the most likely to wear out first as this flap moves a compete travel from end to end each time the car is driven.
Sometimes the electrical contact can be intermittent and only fail when the car is driven due to the vibration of traveling on the road. This can make the flap motor appear OK when its tested with the car stationary but get "stuck" (disabled) when the car is taken on the road. As the temperature flap is moved to full heat when the engine is cold, if there is an intermittent problem, it will be disabled in this position after setting off and cook the occupants when the engine warms up!
The only solution is either repair or replacement. I don't know of anyone who has performed a successful repair.
Unfortunately, "exercising" the flaps doesn't really help as the motors aren't stuck. It only adds to the wear!
Luckily they are easy to change.
Some basic fault readers won't report faults recorded in the climate control module so your "Can Scan" may not be giving you the full picture.
Where are you located? There may be a member close by willing to help you with a VCDS scan?
warm regards
Andrew
