Used to have a car that either lost power on highway or just die suddenly, especially at the stop sign. When the engine went off, it will not start right away, but it will start back on after waiting, may be 5-10 minutes.

It turned out to be a bad Crank Shaft Position Sensor (CPS). Once it was replaced, all the problem was gone. To my understanding it will be very difficult to diagnose the problem exactly other than from signs. Because when it is running you don't find anything wrong. By the time you are running the test it may come back to normal.

CPS needs to be replaced at certain time interval. It may be another thing to look at.