My 99 Honda Accord keeps stalling after warmed up and relay for fuel pump starts clicking rapidly, what could cause this?

Low / uneven idle problem can cause by a lot of components.

Dirty air filter

Dirty injectors + o-rings

Vacuum leak at intake manifold and vacuum hose.

Bad Idle Air Control Motor (IAC)

Low compression (170 psi + is OK)

Start cleaning and repair these trouble spots and see is there any improvement.

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For more advance DIY'er then you may try this.

Use a can of Berryman carburetor clean to locate the vacuum leak.


SEE SAMPLE PICTURE HERE


This is a 20-30 minutes job.

Vacuum leaks can occur in following locations.


Intake manifold AND/OR vacuum lines.


Intake manifold is not accessible unless the engine head if off.

You can still check the potential leak by spraying some Berryman near the intake manifold.

Listen for rpm increase after you introduce the Berryman (FUEL) at idle.


Do the same starting from the brake booster unit (the round unit) on the drive side fire all.

Carefully listen for increase of RPM right after to spray the Berryman to the potential vacuum spot.

Get a friend to HEAR the ROM increase or monitor for RPM on the tech.

DO NOT AIM the Berryman into any heat source.


PLEASE RATE my answer if it is useful to you.

SOUNDS LIKE A VERY LOW IDLE AND THIS CREATES A LOW VOLTAGE THAT MAKES THE RELAY CLICK, DO THIS PROCEDURE:
Here is the common cause of surges, stalls at stops, slow idle speed, erratic idle speed, rough idle and engine hesitation (and other problems), it is in most cases the idle speed control air-bypass valve and or throttle valve and upper intake, these area's get full of gunk and combustion residue over the miles and cause idle issues (stalls, low idle) like yours, Get a can of intake cleaner from any local parts store, not carb spray, intake cleaner, it is made by a company called CRC, remove the air intake hose to the engine, hold the idle high so the engine won't stall, then spray the can of cleaner into the intake while keeping the engine running, use at least 1/2 the can, shut down the engine and disconnect the battery for 5 minutes, then restart and complete a number of mixed driving cycles, town, freeway, stop and go etc., after a few days the problem will go away as the system will relearn to the clean intake.

Sounds like fuel pump might be cloged and its shot and need new one

Sounds like you need a new fuel pump but just check the fuel pump area for all cable connections are in good shape.But i think you gonna need to replace fuel pump.