Mystery brake problem

Hello, my 2001 Kia’s brakes have an extreme amount of play in them. The brake pedal has to be within ~1" of the floor to even engage the brakes, when the pedal is pushed to the floor the car begins to slow down but only at a fraction of the rate it should. It takes WELL over twice the time to stop. The brakes have been bled by 5 separate auto shops in 2 different states. A cracked master brake cylinder was found and recently replaced, still no change. It has progressively gotten worse over the last 3 years. Every mechanic has recognized the problem, yet has no explanation. Thank you for your time and any suggestions.

Does it have drum brakes on the rear? Are the self-adjusters working? How does the parking brake feel? After that, I would replace all the rubber flex lines in the system. One of them could be ruptured and blowing up like a balloon but not leaking. Next, take a second look at that master cylinder…

Does the hand brake work at all? In quite a few cars the rear brakes are adjusted by repeated use of the hand brake. I’d just pull it tight, then release it, a bunch of times. You can just sit in the car and do it anytime. Otherwise, I agree with Caddyman 100 percent.

It turned out that the new master cylinder was faulty! The shop put in another one, the problem was solved instantly. Thanks for the advice caddyman/wentwest