I've seen a bad o-ring in a brake caliper cause this, although that was on a motorcycle. However, the principle is the same.

The o-ring in the caliper is actually square, not round. (So, is it not an o-ring?) When you step on the pedal the pressure goes up and the piston moves out but, up to a point, the o-ring just rotates in its recess and doesn't slide on the piston. When you take your foot off the pedal the o-ring is supposed to rotate back and bring the piston back. That pushes fluid back into the master cylinder and brings the pedal back up.

Again, that was on a motorcycle with the result that the brake lever wasn't coming back out and the pads were dragging on the rotor. Replacing the o-ring fixed both problems. In this case maybe the o-rings in both calipers are old and have lost their "spring"?