There are no fuses for the headlights. The Central Vehicle Electric Control Module controls all of the exterior lighting circuits. It is located to the left of the pedals, above a horizontal row of relays. You can scan the CVECM for fault codes, but may not show any stored DTCs. Regardless, make sure the harness connectors are all OK, especially at the headlight housing.
The failure of the CVECM is not uncommon, and when it happens it is manifest in unique symptoms for each module failure, but generally is by strange behavior or complete failure of operation of one or several lighting functions.
Besides the power supply to the headlight from the CVECM, the ballast for the effected low beam (Dipped,) headlight could be the problem component. It is located mounted to the headlight housing on the bottom. There is no direct diagnostics available, if suspected faulty, a replacement will be the only way to confirm. Did you measure voltage at the HID lamp base harness connector? If that is correct, the ballast is the most likely suspect, but be aware that there is very high voltage used with HID lamps, so extra caution is required. To isolate the ballast as the failed part, try swapping the ballast from the left side headlight and test. If the right side dipped headlight works with the left side ballast, then that proves the right side ballast must be replaced. To avoid a auto headlight range control system error, test with both headlight electrical connectors attached to the headlights, the ballast on the left side does not need to be present during the test,(but being absent temporarily used on the right side, a dipped headlight warning for the left headlight will occur during the test,) to evaluate the right side headlight.

Any more info on this, and or results?

My 2005.5 A4 xenon with adaptive, dips on either left or right. There is little rhyme and reason to how and when it turns off. Turning the light switch off/on, will resolve it for good, or only for minutes. This is a huge safety issue.