1995 Chevy Celebrity engine

The car works wonderfully in town, however. When I get a certain ways out of town and come to a stop sign and apply the brakes the car kills. It starts right up again but then it chugs and sputters for awhile until it is again running fine. Then of course there comes another stop sign 10 miles later and it does it again. I had a mechanic look at it (this was after I persumed there was water in the line and added a can of heat) he didn't know what it was even though it did the same thing to him. He suggested I use Lucas oil trans. Treatment. That hasn't helped either. My car has 39,000 original miles and it's a 1995. Help please!