I have a 99 accord. My brake pedal was soft but I would stop fine and stay stopped with the pedal only about half way in but the pedal would sink a tiny bit when I was stopped. I could also push the pedal to the floor if I wanted.I took it to a honda dealer and another repair shop and both said it was my master cylinder so I had the changed. Now when I push on the pedal to slow down its much firmer and feels like it is stopping better. When I am stopped though I can still push the pedal to the floor. When the car is in park and I push the pedal it is very soft but when the car is moving the pedal is firm and I never have to push more than half way down on the pedal to stop. Does anybody know why I can push the pedal to the floor while it is stopped?
You need to check closely the brake fluid and determine if it slowly going down. I suspect a small leak is a line or a slave cylinder of which you will have 4. Look around and see what is going on with the brake lines. Then as a last resort, you have been sold a defective master cylinder. I might add though that the mechanic that replaced the master may not have done a thorough job of bleeding. I would look at all of these. Good luck!