Hi,
A tricky one. I have had faults to fix like this and these have been due to various reasons; i.e. A phantom powered mic that had been exposed to too much moisture (A numpty had wraped his mouth around it), I have also had a lower grade Mackie (Tapco) amplifier make random noise i.e. clicks/bangs - self generated as some internal component failed; Another more surprising faulty was when a Classic model valve peavey guitar amp started to pick-up/amplify mains-bourne (supply) interference from a lift (Elevator), it was a oil driven lift system with a pump, when ever someone operated the lift loud clicks were amplified through the system. There have also been instances where items like microwaves or fridge thermostats in a nearby kitchen have caused loud clicks if they are on the same power-supply circuit.
Sorry to broaden the horizon of the problem, but in these cases you could spend quite a bit of time trying to isolate the problem by a process of elimination.
Jim.