Why would a car completely lose power while driving but after a jump start back up and remain idled and running?

Does it squeal? A loose serpentine/alternator belt can do that. Also a bad laternator,or poor/loose connections tothe alternator. You need electricity to fire your sparkplugs, and without that your car will stall out. Could also be a short circuit somewhere draining your battery faster than the alternator can keep up with.