Hallway light with multiple switches doesn't always work
I'd start by turning off the power at the breaker, and verifying it's off using a non-contact voltage tester.  Remove the cover plate, and remove the screws holding the switch in place.  Gently pull the switch out of the box, being careful not to pull too hard.  Verify that all the wires are firmly attached, and are not broken or damaged. 

If nothing looks amiss, replace the switch.  If this does not solve the problem, follow the same procedure with each of the other switches.  There should be two 3-way switches, and two 4-way switches.  Be sure to replace switches with an appropriate replacement.  If all the switches have been replaced, and the problem persists. Contact a local licensed Electrician.