Your description of the problem points toward the clutch master cylinder as the culprit. By pumping the clutch pedal you are expanding the primary cup just enough to make it work in the worn area of the cylinder. When the primary cup relaxes, the master shunts fluid during part of its stroke leading to a diminished release of the clutch pressure plate.
Usually the slave cylinder fails by leaking fluid out the boot. Driving symptoms would be a clutch that initially disengages but reengages slowly with the pedal still on the floor and a steady loss of fluid from the master cylinder reservoir.
The reason most people replace both the slave and master cylinder is that both tend to deteriorate at the same rate. So after you replace one component, a month or year later you have to replace the other. In this case you would have to rebleed the system. Also, for a professional mechanic, it leads to comebacks for the same problem.