'01 braking problem, 50k miles

I was driving my wife's Grand Am yesterday and needed to apply the brakes quickly as I didn't see an upcoming stop sign. I was traveling 25 mph. The brakes worked initially but as I was coming to a complete stop I heard a grinding noise and felt it on the brake pedal. As this occurred, the car did not slow down to a complete stop, it kept sliding forward and I let go of the brake pedal and applied it again 2 more times. This happened a few times during the afternoon. At times the brakes worked well and then out of nowhere this problem occurred. It's very dangerous. My wife mentioned the same thing happened to her in August as she was traveling 20 mph and needed to stop for a pedestrian--grinding noise and sliding of the car forward. She took the car into the GM dealer in August and they said the brakes were fine. I can't allow this problem to continue as a major accident is bound to happen. Any advice would be appreciated.

Take it to the dealer again and have one of their service techs ride along with you. That way you can cause the issue and have the tech there to feel it.