What else should I check when troubleshooting a light fixture?
Often with light fixtures, each light has a pair of wires that come up and out of the fixture.  You wire all of the hots together with the line hot, and all of neutrals together with the line neutral.  If the wire nuts that connect all of the wires were not installed properly, it is possible that one of the wires is no longer making a solid electrical connection. It is also possible that one of the wires is damaged.

I would suggest that you remove the light fixture and examine all of the connections.  Look for loose wires (you should not be able to easily pull them out of the wirenut), nicks, burns, etc.  

If everything is visually OK you should test each wire to each socket with a multimeter. Test for continuity by ensuring resistance goes close to 0 when you make a connection. Repeat this until you find the problem. Make sure the power is off when you do this.