The shutters are normally controlled by the CECM which activates a solenoid in the head lamps.I guess the solenoid is getting stuck or there is a wiring fault maybe?
They stay open even when ignition is off?Try shaking / knocking the headlamp assembly, it may close the shutters. Although this is only a temporary fix as they will probably stick open again when used.Is this happening on both headlamps?
See this thread for for info:http://www.golfmkv.com/forums/showthread.php?t=157482The solenoid controller is in the HID ballast itself screwed to the bottom of the headlight. The actual solenoid itself is in the headlight. You could test it by removing the headlight and manually applying power to that solenoid. It's switched on the +12v side so all you'd need to do is apply +12v to it. If you're not getting the light bulb out warning on your dashboard I think the solenoid itself went bad or the wire is broken.Jas