Relay switch keeps shutting off

Sounds like you have an open secret that isn't shutting off, bad relay or broken switch like a brake pedal switch.

This concern is not consistent with fuel pump relay failure. If the fuel pump relay was shorted in a way that powered the fuel pump at all times, the fuel pump would continue to operate but it wouldn't cause the engine to keep running. In order for the engine to keep running, the powertrain control module (PCM) would still need to be powered (along with various input sensors to it) so that it could command fuel injectors to open and ignition coils to fire. In other words, many other parts would need to remain powered-up as well in order to keep the engine running. This prompts the question, "Which component controls when these parts are powered and when they're not?" The answer is the ignition switch. The ignition switch is an electrical switch located on the end of the ignition lock cylinder where the key is inserted. When the key is turned to a certain position, contacts in the switch take power from the battery and apply it to certain circuits associated with that particular switch position. When the switch is turned to the OFF position, power is removed from the systems that keep the engine running. Therefore, I would suspect a failed ignition switch at this time. You can read more here: https://www.yourmechanic.com/article/symptoms-of-a-bad-or-failing-ignition-switch

Open a door . It's suppose to do that . After 10 min. or open a door is what should shut it off . If not ,stuck RAP relay contacts stuck closed . supplying battery voltage all the time . RAP relay - Retained Accessory Power

Relay Controlled RAP
The BCM keeps the RAP relay energized during all power modes, except Off-Awake and Crank. The relay is also energized for approximately 10 minutes after shutting the ignition OFF and removing the key, providing no door is opened.
Relay controlled RAP will end when one of the following conditions is met:
• The BCM receives an input from any door ajar or open switch indicating the opening of any door after the ignition key is out of the ignition.
Important: If the BCM is receiving any door ajar or open signal from those switches when the ignition key is turned OFF, RAP will not initiate.
• The BCM internal timer for the RAP expires after approximately 10 minutes.
• The BCM detects a decrease in battery capacity below a prescribed limit.
Systems powered by the accessory relay during the retained accessory power (RAP) power mode are as follows:
• Power windows
• Sunroof

posible blower resystor and relay is all une piece mounted nes blower motor

there is a bad connection in wiring check that the contacts at the relay are good and tight if that looks ok you will have to check wiring at the sending unit at the tank and any other connector between relay and fuel pump when looking at terminals at relay use a small screwdriver to bend the terminals so they make a good contact try this let me know if this helps you

You will need a new fuel pump relay to keep the engine running. The prime switch for the fuel pump operates fine for it starts the engine and once the oil pressure is up to snuff the computer shuts the prime switch off and turns on the fuel pump relay till you shut the engine off

YOUR AC RELAY IS STICKING CLOSE.CAUSING THE COMPRESSOR TO KEEP RUNNING.SEE WHEN YOU TURN OFF.ENGINE.SOME OF YOUR RELAYS REMAIN HOT ALL THE TIME.LIKE.DRL LIGHTS / BLOWER MOTOR RELAY.REPLACE THE AC RELAY.IF PROBLEM STILL EXIST.YOU HAVE PROBLEMS IN THE HVAC CONTROL MODULE.

Check the fan relays. At the engine compartment. One may be stuck and keeping the fan running.Tap it a little bit before removing it. If it turns of , replace the relays.

you need to check for proper operation at the relay. make sure the relay is getting the cammand.

also you may have a evap temp sensor keeping you shut off. its in side the car usually

That should be just a push to start switch. The start switch is inside the motor. When the motor turns fast enough it trips an internal switch to keep the motor running. It sounds like you have a motor on the way out.