1998 Peugeot 406 peugeot 406 -1998 engine cutting off while driving and would not restart

The car cuts off while driving and would not start. when it cuts off, I have to wait about 10-15mins before attempting to restart. After waiting for 10-15mins and I restart it, it starts ok and drive's fine. But if I attempt to start it before 10-15mins it would not start, it then means I have to wait for about 30mins before I try to start it, then it would start. BUt If I attempt to start it before the 30mins, it means that I have to wait up to 1 or 2 hrs before it will start. The more I try to start it before the (what I call the cooling down period), the longer I have to wait before it starts. I got so frustrated that I had to abandon it last week tuesday after sitting in the car for 3 hours. I called a garage to pick it up the next day, and when they got where it was, it started. What could be the problem, AA had come out 3 times and have giving me different reasons 1. Fuel pump, 2.Crank Sensor, 3. Fuse. The garage is at the moment looking at it . Not sure what it is, any help