I recently drove 1992 Hond Accord LX (120,000 miles, automatic) on a road trip - about 1200 miles in 2 days. Car worked fine, no problems. Got back to the city, spent 1 hr in heavy traffic, stop/go/etc. Brakes worked fine, car stopped well. Then, after a second or two, the brake pedal seemed to get soft under my foot and slowly drifted to the floor (under constant pressure from my foot). This pressure was necessary, or the car started rolling. When the brake pedal was completely against the floor, the car started to roll slowly. I pumped the brakes, and it stopped again. Then the pedal drift. Do I need to replace everything?
I venture a guess that the master cylinder is bad. Open the top of the reservoir and check fluid level. Look for leaks in the brake linkage side of the inside of the car on the floor area. Check around the master cylinder area as well. Then if you notice no visible leaks have someone slowly push on the brake pedal, do you see bubbles? It can be slowly pushing pressure to the brakes but the seals are leaking inside the cylinder. Replacement is most likely the fix, but unless the bubbles are present or a leak noticeable, check the slave unit as well for any leaks. No obvious leaks at the slave replace the master.