Anti-Skid does exactly what its name states. It keeps the tires from skidding. All wheel speeds are monitored. If one has a wheel speed less that the others, it would be treated as a skid and the hydraulic pressure to that brake is reduced (or stopped) until the wheel speeds back up.
Pilots still apply brake pressure as they see fit. The Anti-Skid works without any input from them at all. On a 767 there is no Anti-Skid switch in the cockpit. It's always on.
If the aircraft has Auto-Brakes, it does everything and (not a good idea) the pilots wouldn't have to have their feet on the peddles at all.
Is it possible for the performance of the anti-skid system to degrade over time, and is there a means by which its functionality can be continuously monitored?
No. If maintenance does their job right. There’s no degradation, only failures of components. Once the fault has been identified and repaired, the system is 100% functional.
If things are failing, you get flat and blown tires.
