Q: what causes frequent headlamp burnout?
on 2004 Audi A4

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(2) Answers
I've seen this before on these and VW vehicles. Often times, the mounts for the adjusters inside the headlamp assembly will break, allowing the bulb to vibrate excessively, and consequently, the bulbs to burn out. Unfortunately, the only fix is new headlamp assemblies. If the light pattern oscillates as you drive down the road, or you can't aim your headlamps, then they are broken.
Moisture intrusion if the covers are not replaced, as well as improper installation (touching the glass) is also a possibility.
If you're talking about frequent bulb burnouts it might be caused by handling the bulb with oily fingers. The person at the Audi dealership told me the oil on the bulb causes it to heat up higher than normal and fail more frequently.