all the above stuff is good info... but is it still stalling driving down the road? does it fire right back up?

Interesting topic so far. I'd like to ask if the oil level is low. The oil level sensor can keep the car from starting, I'm not positive if it will stall the engine if it reads a low level. While this isn't directly related to your low pressure. It'* possibly a contributing factor if true.

Since you only plan on having the car for a short time and it'* running fine, you could use an oil treatment to thicken the oil (not typically recommended).

i believe that the OP is related directly to the pwr to the fuel pump....if the car sees that the pressure is low it will cut the pwr to the fuel pump to stop it from working.....and this would make sense in your case