A caller on the show (Tina?) drove a 1990 Honda Civic from Portland to Las Vegas and experienced a loss of brake power. Tom and Ray recommended replacing the master cylinder. I believe that is a fairly safe bet but it is not necessarily the underlying cause.
I had a 1991 Honda Civic and when it was about 15 years old I experience a complete loss of brake power as well, fortunately the emergency brake still worked and I wasn’t going very fast when I discovered the problem. I too replaced the master cylinder, along with the slave cylinders for many $$$. But it turned out the underlying cause was a stuck guide pin in one of the brake calipers, which caused the pads to drag and the disk to really heat up. Resulting in a loss of viscosity of the brake fluid (it became “superfluid” so to speak) and thus was able to leak out when a higher viscosity fluid would not have.
A mechanic told me that the stuck guide pin and dragging pads was a common problem of Hondas of that vintage. So I’d recommend Tina have the repair shop check out those guide pins in addition to replacing the master cylinder.
Good point JesjesRick. Tina should note the temperature of the brake rotors on all four wheels after driving down the road a few miles and not using the brakes. If one wheel is much hotter than the others, this would be consistent with idea that the problem isn’t the master cylinder, but a stuck caliper. It is true that if the brakes get really hot, it happened to me one time driving downhill from the top of Pikes Peak in fact, the pedal becomes very spongy and goes lower than usual. Cooling the brakes returns it to normal. In any event, like Tom and Ray said, this problem needs to be looked at by a mechanic ASAP.