Hi,
The center tab(the contact) has collapsed maybe? Not making contact to
the bulb. Pry them up after turning off breaker feeding the fixture.
Tony

Sarah wrote:

I have a light fixture in a closet that just stopped working.
Replaced all 3 bulbs (have also tested the 'old' ones, and they all
still worked anyway). Have tested each of the bulb 'sockets' with one
of those power testers, and all 3 'sockets' show that the light
fixture is getting electricity, but when I put bulbs in, they don't
light. I know the bulbs work, I tried them in a lamp. If you turn
the light switch on and off, nothing happens, but the power tester
thing will light up/make noise when the switch is in the on position
when each of the sockets are being tested. Make sense to anyone?!?!?!
Help I can't see anything in my daughters closet! Thanks!! Sarah