If you're going from 80 to 15 psi, you could be a victim of some broken nylon timing gear teeth! The pieces of teeth will get sucked up thru the baffle in the oil-pump intake screen, and as you drive, more pieces will work their way up the tube, and slowly block off your oil supply to the pump! When you shut down, *most* of the pieces will fall out of the tube and back into the screen after awhile...Then when you cold start, you have plenty of oil pressure--until the teeth start working their way up the tube! (I say "most" because eventually more and more teeth stay stuck! --been there, done that!--)
The rope-seal can do the same thing, like crazy mentioned--but if you're rear main isn't leaking, that's probably not it!
However, if you're pump is giving you up to 80 psi cold, I think most of us would agree, your problem isn't the pump!