M.,

This is a bit confusing. You have a closet light that is "eating" bulbs.
Is this a new problem? When the bulb originally burned out did you replace
it with the same type of bulb? What wattage bulb are you using? How long do
you run the light in this closet? Are you kids old enough to play tricks on
you? Does the light dim or flicker?
You've already replaced the fixture. I presume you looked at the wiring
while you did this and it was ok. So how's the switch? If the light flickers
or dims replace the switch. Check the wiring at the switchbox and make sure
that the connections are all tight.

Dave M.