Two memorable customer long-standing problems with systems breaking intermittently.
In one case it was finally noticed that the office network connection failed temporarily - when a Harrier jump jet was taking off from the pad outside. Faulty connection in the wall box.
The second was a mainframe crash. Chatting to an operator over coffee - she said "it always happens when I've gone to the toilet". The ladies' toilet had a motor (pump/macerator) which switched on when the toilet was flushed.