1995 Chrysler LHS failing brakes

Your description screams classic rear drum brakes out-of-adjustment, but most of these cars have disc brakes on the rear. By pumping the pedal, you make the next pump before the rear shoes have a chance to fully return, so you get a bigger bite of fluid in the master cylinder. Release the pedal, and wait just a few seconds, and the shoes will retract and you'll have a low pedal again.

Try pumping the pedal up so it's solid, then hold steady pressure on it. You can try varying the amount of foot pressure, but don't release it completely. If the pedal slowly sinks to the floor, internal leakage is taking place in the master cylinder. It will have to be replaced.

Holler before replacing the master cylinder. I have a procedure that requires no bleeding at the wheels; it can all be done at the master cylinder.

Caradiodoc