ABS Light comes on

MY 1995 Grand Prix, has this same problem ever 10 months are so and it is driving me crazy.

It starts fine, then within 30seconds of driving the car starts to sputter, like it is losing power in a way. The gauges shutter back and forth quickly, the lights flicker and if the gas is still be pressed then something kicks back in and then everything is fine. The ABS light will stay on for an eternity until the car is turned off, then the next day I will have the same problem. Now the shuttering will only occur for a few seconds and this drives me crazy on the freeway, it will stop and then maybe 8-10 minutes it will do it again.

Now in the past this has been an indication that either the alternator is bad or that something is wrong with the charging system. Because usually after 3days or so of this I will have trouble starting.

In the past the alternator has been replaced twice and the battery 3times within 3years.

I have taken this to the pontiac people and they can't seem to find anything, and like the old story goes, the problem cures itself in the presence of mechanics so that I look like I am crazy.

MY father-in-law who is very knowledge, has not even the slightest clue of how to fix this problem.

Wondering what is the source of this and if anyone has heard of anything similiar. Could this actually be an ABS problem, my braking system works fine but the lost of power is the main concern.

Thanks.