Light Fixture on ceiling fan

My ceiling fan has four lights. Two of the light fixtures keep burning out the bulbs, almost immediately after I put a new bulb in. Do I need to rewire these two light sockets? Is a short causing this problem?

 

There are many reasons this might be happening, first off what size of lamp is suppose to be in the fixtures and are you using that size? Is there a possibility you may of bought a batch of bad lamps (it happens sometimes especally if you keep buying at the same store)? Watch the lamps in question when you put new bulbs in them and see if they are flickering, that could be a sign of a loose wire inside causing them to burn out prematurely. If changing you bulb supplier doesn't help and you are using the proper ones in the lights then it might be a good idea to check the fixture for loose wiring. Inspect where the bulbs are screwed into the fixture and see if you can spot some type of difference between the two good lamp holders and the two bad ones, such as bad threads, corrosion, etc.
I hope this can help you out a little