What could be shutting off the high pressure fuel pump

!st of all unless you have the experience and the correct tools do not play with the high pressure side of the fuel system. The pressure that is created on the high side is such that will cause serious damage or fatility "Seriously". The system needs to be sealed for the pressure to occure if air is in system" no" presssure.
If lift pump is working(can you hear it?) Is it exiting fuel filter and arriving at inlet of high presure pump at correct pressure. (if not replace filter Use Genuine part. If still no good lift pump or power and earth suspect check. Any engine check lights on? if so use a code reader.(im assuming no light as you haven't mentioned it). If all is good to high pressure pump then you are looking from pump onward. Is this an issue that has just occured or have you purchased vehicle in this condition. Any unusal noises The high pressure pump is driven by camshaft is it actually turning the pump I have come across fractured cams or drives. if ok advise holden to check from here on there may be an electrical issue or injection issue possibly allowing air in system or shutting the pump down. You can check the whole sytem for visible leaks and vacuume connections. good luck.

Fuel pressure regulator . plugged fuel return line .

With the ignition switch ON and the fuel pump running, the fuel pressure indicated by the fuel pressure gage should be 333-376 kPa (48-55 psi).
The Fuel Pressure Check determines if the fuel system is providing fuel pressure. The components involved include the fuel tank, sending unit, pump, pipes and hoses, pressure regulator, fuel rail, and injectors. Also checked is the electrical operation of the fuel pump relay. This chart requires J 34730-1A , Fuel Pressure Gauge J 37287 , Inlet and Return Fuel Line Shut-off Adapters.

Your vehicle has no fuel pump relay . Has a fuel pump flow control module .
Fuel Pump Flow Control Module (FPCM)
The fuel pump flow control module (FPCM) is a serviceable GMLAN module. The FPCM receives the desired fuel pressure message from the engine control module (ECM) and controls the fuel pump located within the fuel tank to achieve the desired fuel pressure. The FPCM sends a PWM signal to the fuel pump, and pump speed is changed by varying the duty cycle of this signal.
Plus it has two fuel pumps !
The high pressure fuel pump (9) is a mechanical one cylinder design driven by an eccentric on the exhaust camshaft (1) of bank 2. High pressure fuel is regulated by the fuel rail pressure (FRP) regulator, which is a part of the high pressure fuel pump. The FRP regulator is a magnetic actuator which controls the inlet valve of the high pressure pump. The ECM provides battery voltage on the actuator high circuit and ground on the actuator low reference circuit. Both circuits are controlled by the ECM. When the ECM deactivates the FRP regulator, both circuits are disabled and the inlet valve is held open with spring pressure. When the ECM activates the FRP regulator, the low circuit driver connects the low reference circuit to ground and the high circuit driver pulse-width modulates (PWM) the high circuit. The ECM uses the camshaft and crankshaft position sensor inputs to synchronize the FRP regulator with the position of the eccentric on the camshaft. The ECM regulates fuel pressure by adjusting the portion of each pump stroke that provides fuel to the rail. The high pressure fuel pump also contains an integrated pressure relief valve.
Your best bet is have it towed to the dealer , you don't want to mess with the high pressure pump .
Pluse

Check to see you have oil up to full on dipstick . The high pressure pump picks up oil at the top level so if oil starts to get to low engine will stop before engine damage . The high pressure pump is what makes the injectors fire . Also check the wires that go thru valve cover some times they burn up and you can smell the burn thru the oil filler cap .

Fuel pump relay is in cavity A in the rear SAM ( Signal Acquisition Module.) on the left hand side of the trunk behind a door.

When did you check the voltage..... you must read it while cranking or you will get a zero voltage reading.. The low pressure tank pump builds pressure to the high pressure pump and then shuts down until a pressure drop is sensed in the low pressure line and it then starts up again.

If rail pressure is too low, it often is the high pressure pump in the engine or the relief valve in the fuel rail. The tank pump is low pressure just to stop the tandem pump from cavitating by sucking too hard.

Mercedes can check the rail pressure and do an injector pressure drop to rule out a leaking injector.

If the tank pump is bad it will require replacement.

Hi.

You connect a fuel pressure gauge like this to the pressure rail. Pressure in this car must be between 35 and 45 psi. If pressure is too low look for kinked fuel lines and eventually replace the pump. If the pressure drops down more than 10 psi in five minutes or if the pressure is considerably higher than that replace the fuel pressure regulator. Below the parts that may need testing:



1. Fuel tank
2. Shut-off valve
3. Non-return valve
4. Fuel pump
5. Fuel pump (Transfer)
6. Fuel filter (High-pressure)
7. Injector
8. Pressure regulator
9. PRC solenoid valve
10. Fuel pump relay
11. Fuel pump resistor and relay (KJ model)

The Bronco has TWO fuel pumps, a low pressure and a high pressure. Low pressure is located in the fuel tank, the high pressure is located....Attached to the LH frame rail ahead of the fuel reservoir.
my guest would be the high pressure pump is getting hot and shutting off, cooled down and starts back up again ??

SYMPTOM/CONDITION:
Symptoms may include no start, rough idle, long crank times, driveway die outs or erratic fuel pressure. A new fuel pump has been released which delivers improved performance. This pump should be used whenever fuel pump failures are encountered.
DIAGNOSIS:
Basic fuel system diagnostics should be used as outlined in the appropriate service manual. A brief recap of the basic diagnostics follows:
Fuel pressure specification - 49 psi - plus or minus 5 psi.
High fuel pressure indicates problems with the fuel pressure regulator. Refer to the service manual for regulator diagnosis. Do not replace the fuel pump for high pressure.
Low fuel pressure - Low pressure could indicate a pump problem or it could indicate a plugged fuel filter or restricted fuel line or no fuel in the tank. Be sure to check these items before replacing the fuel pump.
Fuel System Leak down - When checking fuel pressure be sure to check the integrity of the system after shut down. With the fuel pressure gauge connected, shut the engine off and observe the pressure gauge. The system should maintain at least 24 psi for five minutes after shut down. If the pressure bleeds off quicker, it could indicate that an injector is leaking down or that the pressure regulator is leaking. This can lead to driveablity problems and require further diagnosis.
NOTE: IN RARE CASES WHERE MULTIPLE FUEL PUMP FAILURES HAVE OCCURRED ON THE SAME VEHICLE, A BUILD UP OF RESIDUE MAY HAVE ACCUMULATED ON THE INSIDE OF THE FUEL TANK. THE PRESENCE OF THIS RESIDUE IS NOT EASILY IDENTIFIABLE. THE RESIDUE CAN PASS THROUGH THE IN TANK FILTER AND CONTAMINATED THE PUMP ROTOR. IF MULTIPLE FAILURES HAVE OCCURRED WITH NO OBVIOUS INDICATION OF THE CAUSE, CONSIDERATION SHOULD BE MADE TO REPLACING THE FUEL TANK TO AVOID FUTURE PROBLEMS. PARTS REQUIRED:
I would start here and look at your fuel system closely

The fuel pump runs of the oil sender pressure switch upon starting. Once started the relay takes over from the computers command. If it starts then dies out the relay is bad

First of all, why do you think it is fuel at all, since it could be the ignition?
Second is that if the car shuts down, how do you know it is not simply a clogged fuel filter?
A bad pressure return regulator can blow out fuel pumps by causing the pressure to be so high the pump over works itself.

I suggest you need better data.
A fuel pressure gauge would be nice.
You could improvise one out of a cheap mechanical oil pressure gauge. You could also run some long thin wires to the fuel pump relay output or even to the pump itself, and hang a little LED off the dash as a temporary diagnostic indicator light.
To catch an intermittent, you need constant data.