My 87 300E acted similarly when the plug was melted. Check the condition of it when you pull it off to change the bulb. If melted, you can buy a replacement plug from NAPA and splice it in. No other auto parts store had one when I searched, and MB will only sell the whole headlight assy.

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Rick Miley
99 E300 TurboDiesel
00 Jetta TDI