They want to keep it over night so they can take It for a drive in the morning and give it a workout to make sure it doesn't shut off again. :/ They said we could pick it up around 11.
It turned out the engine had an oil leak, and that oil was saturating the spark plugs and wiring, making the engine shut off because the spark plugs couldn't fire. So they fixed the leak, replaced the gaskets, replaced the wiring and the spark plugs and they said it runs fine now, and hasn't shut off once after being driven for four hours. They just want to play it safe and take it for a few more drives in the morning before they release it to us.
So, yay that they fixed it! Leaving tomorrow (barring any further complications) as soon as I pick up the car and load it back up.
Thanks for all the support and kind words during this frustrating time! You guys are awesome!
(I have to share this picture I snapped of my cat Cammy today - this is totally how I feel about the situation. :P )