The hydraulic system of the brakes is fairly straightforward -- you apply pressure in the master cylinder via the brake pedal's mechanical linkage to a piston in the m/c. In turn, that pressure is transmitted throughout the hydraulic lines, eventually to the callipers' cylinders, which push out the pistons against the rotor. The dimensions (volumes) of the m/c and calipers' cylinders, and the hydraulic lines, are all designed so that the pedal cannot fall to the floor as long as there are no leaks -- pressure would rise a level that you could not overcome with your leg, so the pedal would stop moving at some point.

So obviously, there is a leak. If you find the fluid level in the master cylinder's reservoir has dropped, there's an external leak. Since this is an obvious check, and you haven't reported it, then we can assume there is no external leak, and that you have an internal leak instead -- and there's only one place for that: in the master cylinder. This is a relatively common problem....

You see, the master cylinder is designed so that once you start pressing on the pedal, the cylinder isolates a small volume of fluid from the reservoir, and pressurizes that volume. The isolation of that volume depends upon moving past a seal -- but that seal sometimes deteriorates and leaks, letting the pressurized fluid seep past it and back into the reservoir. Since the volume in the chamber then decreases, you can't develop full pressure, and there's not enough pressure to push against the piston and resist your pedal's movement, so the pedal can move all the way to the floor. While at the same time, since the fluid is just returning to the reservoir, there is no apparent drop in its level or overall loss of fluid to the system.

Change the master cylinder.