Man, sounds like a toughie... Could be a whole slew of things. Next time it dies, check the spark plug boots, make sure they're actually attached to the plug. I've seen 'em work themselves off the plugs before. If it just sits on top of the plug, it will still deliver spark, but if you hit a bump, it might die on you and restart when it settles back down. IDK, just a thought. Is your tank vent working (does your tank look like it's sucked in after some time running). Maybe your start button switch is going bad. Maybe unplug it and test it a bunch of times with an ohm meter. Check all your wiring connections for things like dess post, start button, coil, fuses, etc. I'm tempted to not think it's fuel related because of how suddenly it dies, but I guess it's possible for something to be intermittently obstructing the fuel delivery. Maybe something in the tank/baffle?