Why does the light bulb in the fridge keep burning out?

It may have a poor connection in the bulb holder - perhaps when the door switch asks it to light up the bad connection is causing the bulb to switch on and off - too quickly for you to notice. The extra on/off stress on the fillament might be causing early failures.

This is just a guess - another guess is that your lamp supplier is peddling inferior bulbs.

Another guess is that the door switch is permanently made and the bulb is running continuously and failing when its time is up.

Peccavi
August 2009