The car running supplies vacuum, which gives the power needed. Once you let the vacuum escape (car off, pedal pressed several times,) the brakes do not have the power to create the symptoms.
Check that all of the pads are moving freely , towards the rotor and away from the rotor. I have had pads hung up on rusted locating pins, and the pads do not move, but rather distort as the pedal exerts more and more pressure, and the pedal goes near the floor before it sees full resistance.