1998 Ford Taurus randomly will not start, completely dead

Randomly the car will not start. This can be after driving and stopping, or the first start of the day. There is no pattern but the car does not stall. Once started it always runs. When this no-start occurs, there is no electric at all. Nothing. Removing and replacing the battery terminals generally corrects the problem. Sometimes after removing and replacing the terminals, the lights come on but when I hit the starter it all goes dead again. When I try later it starts. The battery is new and the terminals are clean. I also removed, cleaned and replaced the smaller black wires attached to the negative terminal but that did not help. The car has been consistently maintained since it was new. The alternator is a Bosch replaced about a year ago. The cooling system has been renewed.