Sounds like there might be an issue with the wires at the cluster( central point where all the rods come together). Many of those types of fixyures are put togehter very quickly and there is very little room to work in so the connections don't always get the attention they need. The other cause could be the little bi-pin bulbs. If they came with the fixture, they are not the best quality. While holding the bulb in a tissue, spread the pins very slightly and reinsert back into your fixture. This sometimes helps to make contact with the socket. Make sure that is your bare skin touches the bulb to clean it off as salts and oils from your skin will cause a hot spot on your bulbs and will very likely make them go out a lot quicker.
Andy G
November 2008