Chevrolet: 2000 malibu 3.1 engine shuts off while driving, after stopping the car and turning key off, it starts and runs fine for awhile, then shuts off again

2000 malibu 3.1 engine shuts off while driving, after stopping the
car and turning key off - then on, it starts and runs fine for 5 or
10 minutes, then shuts off again. First time it happened we were on
level city road at 30mph, 2nd time 20 minutes later going downhill,
and third time while on level at 40 mph.

I drove it to the mechanic, he put it on the diagnostics and
everything showed normal. He went on test run for 20 minutes and it
ran fine. Tonite he took it home to see if it willl stop.

Any suggestions as to solutions for this problem