We thought the bulb went out only to find that a new one did not work either. When i got out my tester, the fixture seemed to worked fine in relation to the switch...on/hot, off/not. But no matter what bulb i put in it wont light. I've lifted the tab to get better contact but nothing. When the bulbs are in they show how as well when the switch is on.
You probably need to replace the base (where the lamp goes) in the fixture. Keep in mind that your tester does not draw much of anything at all, so it won't detect a bad connection in the base that shows up when the lamp itself is actually pulling something.
Check also that the connections from the box to the fixture are solid.
If the fixture itself is cheap, consider just replacing it completely. If you continue to have problems, the loose connection isn't in the light fixture.
You can quickly determine this by attaching a pig tail light:
.. directly to the feeders in the light fixture. If the pig tail works, the problem is the fixture (most likely the base). If the pig tail doesn't work, you may have a bad switch, loose neutral, or something else that an electrician should probably inspect.