Starting and keep running.

Somewhere along the line you not getting fuel weather its your fuel pump your fuel filter or injectors

WARNING In almost every case, replacing the Mitsubishi electric fuel pump requires removal of the fuel tank. Please refer to the fuel tank removal and installation procedure at the end of this section.

1. Lift or move aside the carpet in the rear cargo area.
2. Remove the oval cover plate from the access hole.
3. Disconnect the fuel pump harness connector at the rear of the fuel tank.
4. Start the engine, allowing it to run until it runs out of fuel. This relieves pressure within the fuel system.
5. Turn the ignition switch OFF and disconnect the negative battery cable.
6. Remove the fuel filler cap.
7. Drain the fuel from the fuel tank into suitable container(s), each with an airtight lid.
8. Carefully, and using two wrenches on the fittings, disconnect the high pressure fuel line and the main fuel line from the pump. Remove the high pressure fuel hose at the body-side main pipe connection, unfasten the pump-side connection. Wrap each joint in a rag before loosening; some pressure may remain within the system.
9. Remove the fuel pump retaining nuts and carefully remove the pump from the tank.

The fuel pump may still contain liquid fuel. Drain it into a suitable container with an airtight lid before performing any tests or inspections.
To install:

1. Carefully install the pump into the tank and install the 6 retaining nuts onto the studs. Tighten the nuts evenly and in a crisscross pattern to 12 ft. lbs. (16 Nm).
2. Reinstall the high pressure and supply line to the pump.

WARNING Take great care when connecting the threaded high pressure lines. Start the threads by hand, then, while holding the hose side to keep it from turning, tighten the flare nut to 27 ft. lbs. (37 Nm).

1. Connect the pump wiring harness.
2. Connect the negative battery cable. Turn the ignition key to ON but do not start the engine. You should hear the pump running. Allow it to run for about 10 seconds to build line pressure, then start the engine.
3. After the engine has run smoothly for a minute or two, shut the ignition off and check the work area for any trace of leakage. Attend to any fuel leaks immediately, remembering that the system has repressurized and must be handled safely.
4. Reinstall the cover on the access hole and replace the carpet in the cargo area.

diesel engines high pressure pumps not suppose run dry.diesel fuel keep high pressure pump cool and lubricated.problem could be fuel pressure regulator in the fuel filter water separator housing.replace fuel filter see if it helps problem could be fuel pressure regulator in fuel filter housing, the fuel pressure regulator has a air bleed orifice that allows vent to the fuel tank.make sure fuel pump fuse okay pump getting power. i would let garage or dealership check it out if all fails because your diesel engine fuel timing is pcm controlled if let fuel system go dry you probably have to have fuel injection timing reset or could have damage high pressure pump letting it run dry i hope thats not the case because high pressure pump not cheap part i hope it not that.

Your fuel pump is in tank and is electric. Rock Auto online shows pics and another possibility is fuel pump relay (they show it also)

See Figure 1
Two different electric fuel pump configurations were used on fuel injected models. One consists of a low pressure in-tank boost pump in conjunction with an external, frame-mounted high pressure pump. The low pressure pump is used to provide pressurized fuel to the inlet of the high pressure pump and helps prevent noise and heating problems. System pressure is controlled by a pressure regulator mounted on the engine.
The other configuration consists of an in-tank high pressure pump which does not utilize a boost pump.

Fig. Fig. 1: Disassembled electric fuel pump

REMOVAL & INSTALLATION

In-Tank Pump
See Figures 2, 3 and 4

1. Disconnect the negative battery cable.
2. Depressurize the system and drain as much gas from the tank by pumping out through the filler neck.
3. Raise and support the rear end on jackstands.
4. Disconnect the fuel supply, return and vent lines at the right and left side of the frame.
5. Disconnect the wiring to the fuel pump.

Fig. Fig. 2: Low pressure in-tank electric fuel pump

Fig. Fig. 3: High pressure in-tank fuel pump

Fig. Fig. 4: Removal of electric fuel pump

1. Support the gas tank, loosen and remove the mounting straps. Remove the gas tank.
2. Disconnect the lines and harness at the pump flange.
3. Clean the outside of the mounting flange and retaining ring. Turn the fuel pump lock ring counterclockwise and remove.
4. Remove the fuel pump.

To install:

1. Clean the mounting surfaces. Put a light coat of grease on the mounting surfaces and on the new sealing ring. Install the new fuel pump.
2. Installation is in the reverse order of removal. Start the vehicle and check electric fuel pump operation. Check for fuel leaks.

High Pressure External Pump
See Figure 5

1. Disconnect the negative battery cable.
2. Depressurize the fuel system.
3. Raise and support the rear of the vehicle on jackstands.
4. Disconnect the inlet and outlet fuel lines.
5. Detach the electrical harness connection.
6. Bend down the retaining tab and remove the pump from the mounting bracket ring.
7. Install in reverse order. Make sure the pump is indexed correctly in the mounting bracket insulator. Start the vehicle and check electric fuel pump operation. Check for fuel leaks.

Fig. Fig. 5: High pressure external fuel pump

if power fine and no fluctuation than the pump itself is problem or problem with filter new doesnt mean cant be faulty also listen to pump if hum goes high /low than pump is surging and is faulty if pump stays steady and pressure test is steady when teted before fuel filter than problem with filter or line

Before you replace the filter, you should have whats called a mass airfflow sensor. This will be located on between the airfilter and the intake manifold (throttlebody/accelorator). Take a small screwdriver and with the handle, lightly tap on it (with car running, if possible); and see if the idle changes, hesitates, or the car dies. If so, replace it. If not, purchase of MAS cleaner (MAS is Mass airflow sensor) and clean the inside of the sensor. This will have a honeycomb shaped inner, and rest assured this spray will not harm the sensor as it's formulated for it. Spray it generously and let airdry for about 15 mintes. Reconnect the MAS, and it's wiring harness. If the car still stalls, or does not stay running, proceed to replace the fuel filter which is located (usually) on the driver side next to the fuel tank. (you may need to remove the rear tire for better access).

Also, find your fuel rail, and ensure you are getting fuel pressure. You will see a round (usually black) nob. Unscrew this (counter clockwise) and depress the needle inside (covering with a rag slighly as not to get fuel spray in your face or clothing). If you have fuel pressure (if it sprays), then you're fuel pump and fuel pump relay should be good. However, if you do have pressure, and the new filter made no difference, replace the fuel pump relay, and the fuel pressure regulator.

Please let me know if you need further assistance, as well as to wither or not any of these helped fix this issue.

Sincerely,

carsandcomps,

Guru, Premium Expert @ Fixya.com

CHECK SHRADER VALVE ON FUEL RAIL FOR PRESSURE. IT IS COMMON FOR PUMP'S TO GO OUT. YOU CAN HAVE SOMEONE LISTEN TO TANK FOR A BUZZ NOISE ON KEY CYCLES OR TEST FUEL PUMP CONNECTOR HARNESS FOR POWER. TRY KEEPING AT LEAST QUARTER TANK AT ALL TIMES TO KEEP FUEL PUMP COOL,SOME PEOPLE DRIVE ON LOW AQLL TIMES AND KEEPS PUMP HOT CAUSING PREMATURE FAILURE.

Possibly water in the tank and some other contaminant in the tank....possibly failing...clean filter is easing flow and pressure function from your fuel pump.

just for you REMOVAL & INSTALLATION
See Figures 1 and 2
WARNING In almost every case, replacing the Mitsubishi electric fuel pump requires removal of the fuel tank. Please refer to the fuel tank removal and installation procedure at the end of this section.

1. Lift or move aside the carpet in the rear cargo area.
2. Remove the oval cover plate from the access hole.
3. Disconnect the fuel pump harness connector at the rear of the fuel tank.
4. Start the engine, allowing it to run until it runs out of fuel. This relieves pressure within the fuel system.
5. Turn the ignition switch OFF and disconnect the negative battery cable.
6. Remove the fuel filler cap.
7. Drain the fuel from the fuel tank into suitable container(s), each with an airtight lid.
8. Carefully, and using two wrenches on the fittings, disconnect the high pressure fuel line and the main fuel line from the pump. Remove the high pressure fuel hose at the body-side main pipe connection, unfasten the pump-side connection. Wrap each joint in a rag before loosening; some pressure may remain within the system.
9. Remove the fuel pump retaining nuts and carefully remove the pump from the tank.

The fuel pump may still contain liquid fuel. Drain it into a suitable container with an airtight lid before performing any tests or inspections.
To install:

1. Carefully install the pump into the tank and install the 6 retaining nuts onto the studs. Tighten the nuts evenly and in a crisscross pattern to 12 ft. lbs. (16 Nm).
2. Reinstall the high pressure and supply line to the pump.

WARNING Take great care when connecting the threaded high pressure lines. Start the threads by hand, then, while holding the hose side to keep it from turning, tighten the flare nut to 27 ft. lbs. (37 Nm).

1. Connect the pump wiring harness.
2. Connect the negative battery cable. Turn the ignition key to ON but do not start the engine. You should hear the pump running. Allow it to run for about 10 seconds to build line pressure, then start the engine.
3. After the engine has run smoothly for a minute or two, shut the ignition off and check the work area for any trace of leakage. Attend to any fuel leaks immediately, remembering that the system has repressurized and must be handled safely.
4. Reinstall the cover on the access hole and replace the carpet in the cargo area.

Fig. 1: Components of the fuel pump and fuel tank Fig. 2: Components of the fuel pump-all models similarTESTING
When diagnosing engine problems, particularly a "no start" condition, the fuel pump function should be checked. Because of the difficulty in reaching the fuel pump connections, Mitsubishi automobiles have a conveniently located test connector under the hood. V6 Monteros have the connector taped to a wiring harness inside the right front kick panel, near the ECM and relays.
This connector bypasses all of the controls in the system (ignition switch, pump relay, etc.) and sends voltage directly to the pump. When power is applied to the pump you should be able to hear it running, although the in-tank pumps require you remove the fuel filler cap and listen at the filler.
To use the test connector, make certain the ignition is OFF. Great damage may be caused if the system is tested with the key on. Locate the test connector in the engine compartment (on later Monteros it is located under the right-hand side of the dashboard)-it is generally on a short lead out of a wiring harness and looks like a plug that isn't connected to anything. Once found, use a jumper wire to connect the test terminal to the positive battery terminal. Listen for the fuel pump; if it runs, you know the pump motor is good. While the pump is running, gently squeeze one of the fuel lines and confirm that the pump is delivering fuel pressure. If it does not run, the pump itself is most likely defective OR the connector to the pump is faulty.
When the pump is removed from the tank, it may be checked by applying battery voltage (+) to the connector and grounding the housing. Only run the pump for one or two seconds during this test; the pump can be damaged by running without liquid.
CAUTION Make certain the pump has been drained of residual fuel and is free of fuel vapors. Connecting and removing the test leads will cause sparks which can ignite any vapor in the area.