If the brakes work "normally" when essentially cold (early applications, stationary with engine running), and apparently degrade when under severe use, I'd think of heat boiling the fluid in the wheel cylinders (calipers). Pumping the pedal when hot overcomes the presence of "gas" (at this time we are talking of gaseous brake fluid, not "air" as in unbled air from assembly) and super compresses it so you have a solid pedal during THAT application. As soon as you release the pedal, the gas resumes its original volume (compresses, then expands), and the pedal is again soft.
As that volume of gas cools, it returns to the liquid state, and the pedal again feels normal (solid).
Incidentally, all discussion here should deal with only regular brake fluid, not silicone brake fluid, which is another animal entirely.
You should also look for evidence of excessive heat on the brake pad material, and the calipers. I had problems with cooked seals, cracked rotors, and warped pad backing plates. Ours was very evident, but we never had boiled fluid. We also had huge ducts to the calipers.
I'd look elsewhere for the problem than the master cylinder. The most common failure of the master is that the seals leak BETWEEN the cylinders, causing the pedal to slowely move to the floor, WITHOUT any external leakage of fluid. If your cylinder is dry on the outside, and under the dirt seal, AND at the firewall where the brake booster enters the cockpit, then the problem is not the internal leakage of the master cylinder.
Solution to the boiling fluid problem is:
-Higher DOT grade of fluid which will raise its boiling point.
-Cooling ducting to the calipers, hopefully to the center of the disc for ventilated style of discs, and the edge of the disc for uniform cooling of the solid style.
-Brake fluid re-circulator system returning to the master cylinder...illegial in IT, I believe.
-Water spray bars on the disc. I saw them used on an ITE car for an enduro...big tank in the back seat.
That's about all I can think of that this time. Hope it helps.
Good racing.
Bill