on a two light bathroom light scone. One light stopped working?

I have a two light bathroom scone over the sink in my bathroom. Both lights had burned out. I replaced them both, but one side will not work. I thought it might be the part where the light buld was screwed into, but it appears to be solidly placed within the fixture. I figure I might have to take off the fixture to insure that no wires have come loose. ANy suggestions?