could be a break in the bulb itself, but the electrical force fuses the two ends that are broken for that momentary time untill you turn the car off, i had this happen in my honda civic way back when, if you looked at the bulb it looked all fine, but it was actually broken. i would notice it wouldnt work at first start up but after a while i noticed it would be working.
my first suggestion is to try changing the bulbs, second thing is to investigate further for a loose connection.
OH and welcome to bmw forums, i am gonna move this thread to its proper location. e46