There are two things to consider. First, if you have rear drum brakes, the symptom could apply to rear shoes out-of-adjustment. The second and more likely cause is the car has anti-lock brakes, and a scanner is needed to command the computer to open two valves so those chambers can be bled, then you have to continue bleeding at two wheels.
That problem is caused by bleeding at the wheels when you replace the master cylinder, or when you allow the master cylinder to run empty when a caliper is removed. All of that can be avoided with a couple of simple tricks. Some people do not realize you need to bench-bleed the new master cylinder, but before you remove the old one, loosen the line nuts just a little, unbolt the master cylinder and slide it off the mounting studs, then use it as a handle to bend the steel lines upward a little. That will stop the brake fluid from running out of the lines. Now remove the master cylinder and install the new one. Snug the line nuts, bend the lines back down, then bolt the new master cylinder to the booster. Now, loosen one line nut about half a turn, then have a helper push the brake pedal very slowly, half way to the floor. It should take fifteen to twenty seconds to get there. Once there, tighten the nut, then have your helper release the brake pedal quickly. Do that a second and maybe a third time until you no longer see any air bubbles coming out by the nut, then do that for the other line.
By pushing the pedal slowly, brake fluid gets pushed down the line, and air has a chance to float back up. When the pedal is released quickly, the fluid rushing back into the reservoir will wash any air bubbles up there with it. This can even work without loosening the line nuts if you catch the low fluid just as the reservoir is running empty. At this point, no air made it down to the ABS hydraulic controller so you will not need a scanner to bleed that unit.
Now replace the calipers. It should only take a few minutes once the hose is disconnected from it, but sometimes we run into problems that take more time. Gravity is going to suck the brake fluid from the reservoir, and if you do not stop that, you will have a very time-consuming bleeding job in your future. The trick to prevent that is to place a stick between the seat cushion and brake pedal to hold the pedal down about two inches. That places the master cylinder's rubber lip seals past the ports leading into the reservoir. Gravity will not be strong enough to pull brake fluid past those seals. You do have to watch that brake fluid does not siphon out of the rubber flex hose. That can be minimized by tying the end up as high as possible until you are ready to connect it to the new caliper.
I only use gravity-bleeding by myself when bleeding calipers and wheel cylinders. Some people think this must be done with a helper pushing on the brake pedal, and when they do, it is customary to push the pedal all the way to the floor. That is what damages a lot of master cylinders. Crud and corrosion build up in the lower halves of the bores where the pistons do not normally travel. When the pedal is pushed to the floor, those rubber lip seals are run over that crud which can rip them. Typically that causes a slowly-sinking brake pedal, and that often takes two or three days to show up. This is not a concern with your new master cylinder, or with one that is less than about a year old. This damage also commonly occurs when a driver is suddenly surprised by a leak and pushes the pedal to the floor in a panicked attempt to stop. For that reason, when writing up a repair estimate for a ruptured rubber flex hose or steel line, a lot of shops automatically include a rebuilt master cylinder in that estimate. Some install a new master cylinder without question to insure the quality of the repair. Some will explain later the new master cylinder was not needed, but that often comes back to bite them in the butt when the fading brake pedal shows up days later. Those mechanics who do not include the master cylinder in the estimate run the risk of having to tell the customer later that more parts are needed than were first thought. They tried to keep the cost down, but they end up looking somewhat incompetent for not finding that right away. If they want to go that route, they are better off explaining this issue, then letting the owner decide. That way if it turns out later a new master cylinder is needed, they are aware of why already, and the mechanic gets to look good for attempting to save them a few bucks.
In addition to this great and wondrous information, here is a link to an article that might give you some more ideas:
Saturday, June 9th, 2018 AT 8:20 PM