Could be main relay, cutting in and out sometimes sending fuel, sometimes not, but not sure. Is ECU throwing codes? CEL does not always come on even if ECU is throwing codes. If not main relay, then check rotor, cap, wires, and plugs. If that still doesn't help, then i would check injectors, they may be good when cold, but when warmed up, injectors may fail, and cause you're car to run poorly, and look for possible causes for injector problems, like fuel filter or poor connections. Just my .02. Good luck.