1998 Cadillac Deville Car engine dies when de-accelerating

While driving my Deville, long trips, shorts trips, when I de-accelerate at stop signs, or slow down to make a turn, the engine dies. I lose power steering and braking. Had it checked out by many mechanics. Each one says something different. Each has worked on the problem and done what they think is wrong with it to fix the problem. Sometimes I can drive it for 4 or 5 days and nothing happens, then it will start the dying process all over again. Sometimes it will start right back up, but sometimes I have to let it sit for 5 minutes before it will start. Please help! My wife refuses to drive the car because she cannot manage the steering when the engine dies. Thanks!