My Ford econoline  van with fuel injected 5.0L and 187000 miles. Has acceleration hesitation when engine is cold,not when engine is hot.  and slight rough idol, and the issue of continuing to run reliably,  issues.  I have narrowed my focus to the fuel system.

I'm just the vehicle's owner and not a pro- mechanic, but I try and do as much repairs myself.

I would like to know, what should I look into being the problem s, because my fuel pressure is dropping off, when the engine is not running. Fuel pressure starts at 42psi.  When I remove the vacuum line from the pressure regulator  pressure climbs to 52psi. reconnect the vacuum line and pressure drops to 42psi. There is no fuel present or leaking  from the vacuum line or the pressure regulator.

With the engine off, and fuel lines pressurized to 42psi, the pressure will drop to 35psi within 4 minutes, then to 25 psi after 6-8 minutes. Is this normal? or what could be causing this pressure drop? should I be concerned about the pressure drop shortly after the engine is turned off?

I replaced the MAP sensor, and that has helped the idol issue. 

Thee is no Mass air flow sensor. Vehicle is located in NC, USA.

The fuel filter is 1 month old.

The high pressure fuel pump is new, having been installed just 2 weeks ago.

Engine starts right up when key is turned. very little engine cranking is needed.

Engine does has a slight amount of shake when idling, that can be felt through the valve covers, and heard at the engine's side. I'm thinking it is a miss or two. Could dirty fuel injectors cause that?

Could faulty or dirty fuel injectors cause the fuel pressure drop when engine is off?