This problem is caused by loss of contact between the terminals in the bulb receptacle and the lamp assembly. Look closely; you may see some discoloration at the contact area due to arcing.

To solve the problem you need to re-establish contact by locating these two terminals.

The terminal on the bulb receptacle is obvious but the one on the lamp housing is not. The lamp-housing terminal is a small metal strip (2-3mm wide) that is snapped into the housing. It is located on the outer edge of the bulb hole.

Solution: Get a flat head screwdriver or small putty knife. Carefully pry out the lamp terminal strip out of one snap hole closest to the bad bulb. The terminal will feel loose and can make contact easier. Clean the bulb receptacle contacts. Re-install the bulb and problem should be fixed.
You may apply epoxy glue to hold the strip in place.

BTW, make sure bulbs are the correct specification. Use only OE or Osram bulbs