Problem with a 1992 Honda Accord staying started

I have a 1992 Honda Accord LX. I was sitting idle one day and the car shut off. I tried starting it again, and it would start, but would
not stay started. Before this there had been problems with the car gaining speed, it seemed like I had to fully depress the gas pedal, but I put some fuel injection/filter cleaner in and that went away for a while. Is it the fuel pump, relay system, filter...Any thoughts would be greatly appreciated.
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