96 GMC Safari: Coasting stops / Unresponsive brake pedal

I have a 1996 GMC Safari van, mileage 103195. I keep running into a problem where, near the point of stopping, the brakes suddenly seem to fall out from under me. The pedal becomes somewhat unresponsive, and I can feel it coming back toward my foot, but during this time I cannot stop unless I violently slam on the brakes.

I took it in for repairs, not knowing the cause, and had some work done, but still was experiencing the problem. I took the mechanic for a drive in it and he claimed that it was simply the ABS pump kicking on and that this is normal. If I kept my foot on the brake and didn't freak out, I'd stop like I should.

I took his advice, but there have been two occasions where it seems like no matter what I do, I cannot get the brakes to work in a safe amount of time. I am afraid of an emergency situation in which this may happen.

I have encountered numerous explanations, including the master cylinder, and the ABS codes in the van's computer (see here: http://www.brennanlaw.com/lemonlaw/absjury.htm). The van's guide book seems to echo the mechanic (keep your foot on the brake and everything will be OK), but I'm not convinced this will be entirely true in an emergency.

Is this fixable, and if it is, what on EARTH am I supposed to do about it?