Mystery brake problem

Occasionally and randomly, the brake pedal feels solid and will not depress. There is a very slight vibration and faint whirring sound when this happens. Keeping a foot on the brake pedal, a few seconds later the pedal vibrates a little bit more and the problem clears. Alternatively, pumping the pedal a couple of times and the problem clears. It seems as if something is causing an obstruction to the mechanism. I have had two mechanics try to investigate, but as the problem is random and has not occurred during their inspections they have been unable to diagnose a cause. They have inspected the brake system in general and report it is in good condition as is the whole car considering its age. Luckily my boy racer days are long behind me so emergency stops are almost never necessary, but of course it could lead to an accident eventually.