1988 accord wont stay turned on

[Xaisk]

I put the key in the ignition and start the car, Sometimes itll start right up but other times itll take a few trys while pressing the gas pedal. (I know its not the fuel pump or filters as i replaced those a few weeks ago. ) After it does get turned on, the car will stay on for awhile and slowly die out and turn back off. Anyone know why? I am currently doing work on it and putting in a few new gaskets so the engine is in pieces right now. I have a theory on it possibly being the vacuum hoses as they are old and dryrotted but no holes in them are visible. I plan on replacing them sometime within this week. Help would be Appreciated.