Pulsing pedal with no braking sounds like a faulty ABS sensor or wiring to me.
I've had the same thing happen to me before when I had (intermitantly) faulty wiring to the front right ABS sensor. Normally ABS is supposed to disable itself below a certain threshold speed - approximately 20Km/hr.
Why ? Because the whole way ABS works is by measuring the speed of each wheel, taking the fastest rotating wheel as the "road speed", and any wheel that is doing a much slower speed than the fastest wheel, or not turning at all due to locking up has its brake pressure momentarily removed to allow the wheel to spin up again and regain traction.
(There's more to it than that but thats the basics)
If the ABS didn't disable itself then you could never fully stop - because stopping implies all wheels have stopped turning.

So the way around that is that below a certain threshold speed the ABS deactivates, to allow you to fully stop.
My theory of what happens is that a faulty sensor and/or wiring can cause extra spurious pulses to be sent to the ABS computer from that wheel, thus making the computer think you're going faster than the threshold speed.
For example say you're really doing 10Km/hr and trying to come to a stop, but extra pulses from one wheel make the computer think that wheel is doing 40Km/hr.
The computer will assume you're doing 40Km/hr with 3 of your wheels locked up!

And of course it will release the brakes on 3 of the wheels. (Since the rear wheels are controlled together, if a rear sensor is faulty it will effectively release ALL the brakes)
After about a second the computer will usually realise there is a fault condition and deactivate itself (thus re-activating your brakes, and bring up the ABS light) or the fault condition itself may go away. (wires flexing with suspension movement etc)
Unfortunately FINDING which wheel it is can be very difficult if the fault is only transient... I wasn't able to find which wheel it was on my car for months until finally one day the ABS light came on permanently and by measuring the sensors from the ABS plug I worked out it was the front right sensor and fixed it.
I've had no more occurances of this "momentary missing brakes at slow speeds" problem since fixing it...so I'm fairly confident that spurious signals to the computer is what causes it...
Regards,
Simon