The fuel pump is relatively new and when running, the fuel pressure is good (50 psi plus).
However, when the engine is shut off, the rail pressure drops way off. It requires a lot of cranking to get the pressure back up when starting the engine.
There doesn't appear to be any leak in the fuel line between the fuel pump and the fuel rail.
I am reluctant to install another fuel pump (new $300) on a vehicle this old.

 

With no visible leaks and no heavy fuel smell under the hood I would say the pressure regulator on the pump is leaking.