Have you checked for spark and fuel? I bet you'll find one is missing when it dies! It could be the ignition module or coil, or a fuel pump. You won't know till you do a little diagnostic work.
my Duster used to do the same thing back in the '90s, it felt like the tranny/converter was locking up and stalling the car-would start up again right away, and never stalled while the car was moving. Turned out to be the ignition module.
