My center brake light worked with no problems, but then I had my brakes changed and now the center brake light now works sporadically. What could be the problem.
This is most likely a separate fault that just happened to occur now.
If the other brake lights are functioning correctly, then the fault lies with either the wiring to that lamp, a loose connection in the wiring or an internal fault in the lamp.
If the other brake lights also mess around, check the switch and wiring.
Edit : as GdD has pointed out, the only common point is the brake pedal, the rest of the systems are separate.