I've seen and dealt with radar failure both at Heathrow Tower and the old LATCC at West Drayton and not too many lives were lost. I believe that separate power supplies are employed, say for every other display, so that it should not possible for all screens to go blank (says he). Controllers can always peer over their colleagues' shoulder... in a state of utter terror!! It never lasts (too) long though and the backup flight progress strips are a God-send. Now don't dare ask what happens if the new electronic flight progress strips pack up...
Probably worse than straight radar failure was bad weather on radar back in the old days when heavy rain would virtually blank out the screen and there were no SSR labels. Didn't need Ex-Lax after that.