I had this exact problem with the same model and it drove me nuts. By the time I could get any tools to the car, it would run again. It finally stayed dead long enough to determing that the coil was shorted internally and apparently when it got hot. Try a new coil.
I had a similar problem with my 1987 Aerostar. I suspected it was either the ignition module (on the side of the distributor) or the fuel pump (located in the gas tank). I carried another ignition module and the tools to install it, and a fuel pressure gague and waited for the problem to happen again. In this case, it turned out to be the fuel pump.
I HAVE THE SAME VAN IT IS THE FUEL PUMP WHAT HAPPENS IS THERE IS ENOUGH PRESSURE TO GET THE VAN RUNNING BUT SOON THE PUMP RUNS OUT OF PRESSURE AND IT STOPS RUNNING IF YOU LEAVE IT LONG ENOUGH IT WILL START UP AGAIN BUT SOON THE SAME THING HAPPENS AGAIN.DON'T WAISTE YOUR MONEY ON IGNITION PARTS I DID ALL FOR NOT
Died while driving? Alternator
if it won't start up again chances are it's probably your fuel pump
A universal joint on the driveshaft going bad.
Stalling while driving may be caused by a collapsing or kinked neoprene fuel line.
Check timing belt
Bolts might come loose from the transmission pan while you are driving your 1987 Ford Aerostar because they have not been torqued to specified tightness. They might also come loose because the bolts are not the right size or are worn.
The reason your 2001 Hyundai Sonata lost all power while you were driving and stalled and won't start again is either the battery or the alternator. If you have no power you most likely have an alternator problem.
A faulty alternator will cause those symptoms. You might want to get t checked out.
Have someone check your fuel pump pressure,if you lose fuel pressure while driving,and then it comes back that would explain why it seems to start by itself.
probably it had no gas or it was just to old
If you lost power while driving and it did not start again, it could be an alternator issue. Double check the battery just to make certain it isn't an issue with the cable connectors too.
Your car lost power while you were driving and it will not start now because the battery is depleted.