sounds like fuel isn't reaching its destination. Tilt the car backwards(uphill) and the fuel will run away from the pump? Point it down forwards (downhill) and then the fuel will run towards the pump...it makes legitimate sense. So you may want to get the fuel pump checked out. Let it sit, the fuel will trickle out of the lines whereas starting it again after just driving it, there is still fuel left in the lines as it hasn't had a chance to dissapate.
I don't know for sure, but do you have to wait a moment between turning the key, then actually starting the ignition? My friends diesel truck requires about 5-6 seconds before actually starting the truck. Turn the key to the battery position and a little light comes on and says "wait to start" then shuts off telling you to start the truck at that point. Maybe that pumps fuel to its destination to start...this is just an idea???
5 Speed Manual
Alpine CDA-7895 Head Unit
12" Alpine Type-R, sealed box
Pioneer 400w amp for $20 at a yard sale (to replace my fried MRV-1507)
Infinity Kappa 4" 2-way speakers(rear)
Infinity Kappa 5.25" component speakers(front)
Debaffled airbox, K&N filter
Tracked Mud on carpets
Shampooed and cleaned carpets