The fact that the OP hasn't been on here since the day of the original post should tell us to let sleeping dogs lie.
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That's why i say: Remove the oil pan, check condition and swap oil-ring and relieve valve....I wonder if you have some debris floating around in the pan and it will get stuck on the pickup screen and starve the pump. When you shut down the engine, it falls off and gets back into the pan - then repeat. Just a thought.