Over voltage will kill filament lamps, get a DC voltmeter and measure your
voltage at the battery, you're looking for about 14.0 VDC with the engine revving.
That would not explain why a single lamp would die, but see what you have since if
it's too high you need to fix it.

Is the lamp flickering? maybe a loose connection? Perhaps a flaky bulb out sensor relay contact or loose crimp at the connector.
Is the bulb out sensor lamp working? see if it comes on when you start out.
Look to see if it's triggering.

Touching a quartz halogen lamp puts skin oil on the glass, the high temp reached
with those lamps will discolor it. If you do touch it, wipe it off with 90%
isopropyl alcohol that you get at any drug store.

Bill