Another possibility is that the rotor that carries the spring loaded vanes has excessive wear/clearance in the body of the pump itself.
The rotor has 2 diameters where it runs in the cast iron pump housing,and you'll usually find that there are 2 grooves worn in the pump body itself.This may contribute to loss of priming and/or oil "pressure".
It's an easy fix if you have a lathe,or access to one,just set the housing up,bore it out(usually a 1/16" cut is plenty),then make either a phosphor bronze or cast iron bush to suit.With a couple of thou clearance this should solve the problem.
But as previously posted,check the spring that fits in the vanes,they can fail.