[f5fstop]

I have heard it happening to other vehicles (GM as well as Ford/Chrysler and yes, the never break Honda and Toyota), but not the H3, until your post.
My recommendation would be to call the assistance center and let them know this is happening. It is a safety problem...big time.

In defense of the dealer (something I'm not known to do), if a dealer cannot recreate the problem, it is hard for them to fix it.

The problem might be as simple as a wire losing contact, or as complicated as a computer with a defective circuit board. Most problems I have heard of were due to ignition systems shutting down, or fuel pumps shutting off. However, with a shut off fuel pump, the car will not immediately go dead, it will sputter until all the fuel is burned, then go dead. Electrical problems go dead instantly.

Now, a few questions.
Do you remember if every time this happened you hit a bump or a pothole? If you have a wire not connected correctly, sometimes a sudden jolt will break the electrical connection, then when you pull over, it starts. Same with a circuit board inside a computer, but not as likely.
Did you go through a lot of water (probably not the cause but who knows).

Those are the only two items that come to mind.