As an former Navy electrician without any sort of certification, here's what I would suggest:
Turn off the power to the circuit at the breaker, dissasemble the offending light since it appears that this is the only component affected. Check for loose connections. In fact, it's probably a good idea to disconnect the wires, clean them up and reconnect them. This is important, as a bad connection will produce heat which can burn your house down. Re-assemble and try the system again.
If it still won't work, secure power (navy term meaning turn off at the breaker), and check the connections at the switches. I'm assuming that this is a two-way system where each switch turns the lights on and off. Make sure all the connections are clean and tight again. Try the system again.
If that don't work, the wires connecting the light to the rest of the circuit may be damaged and may have to be replaced. Figure out where those wires connect to the rest of the system and check those connections.
Basically:
Safety first! Always shut off the breaker before messing with wires!
Start from the problem component and check everything that could be bad. Start with the cheap and easy and single pointfailures which could cause the problem.
Another helpful idea if you get stuck is to draw out a diagram of the system (if you can), and look for possible problems.
I hope this helps.