I don't think there is a check valve, but I haven't heard that you can lose the prime on the lube oil side. The oil always drains mostly down into the sump. My guess would be that your oil pump is weak and what happens is that it only works enough when it has oil in it, but when the oil drains down, it is not strong enough to suck up the oil at first.
So I would take off the pump and clean it up and see how it looks in there. There is a piston in the pump that is held and pushes against a spring so maybe the spring is tired or the piston scarred.
Sort of an odd problem.