Brake pedal stops normally then slowly fades to floor. Master cylinder? Booster?

[Anker]

This really has me stumped. The master cylinder is the only place where fluid can leak out of the pressurized part of the system without the fluid leaving the system and eventually leaking to the ground.

When the brake isn't activated the reservoir and the brake lines are connected. As soon as you press the pedal the connection to the reservoir is sealed from the brake lines by the piston in the master cylinder. All the the booster does is to assist the master cylinder in pressurizing the brake lines by using vacuum. Any fluid leaking past the piston in the master cylinder will end up behind the piston, which is now connected to the reservoir.