Randomly starts misfiring while driving. Intermittently misfires or drives normal when you start the car. New spark plugs, new coils. Check engine light some times comes on. Doesn’t give cylinder identification or direction codes. Mechanic doesn’t know what’s causing it or how to fix.
You need a mechanic with more experience in troubleshooting the CEL system. Random misfires can be tough. I was troubleshooting my wife’s car for the same problem when she called with the answer. The gas station where she buys her gas had told her that they had water in their gas tanks from flooding in the area. They refunded her money for the gas purchase and I drove the car until the misfire went away. We now buy all of our gas from a station on top of a hill. I suggest finding a good independent mechanic with experience in CEL problems.
Could be as simple as low fuel pressure or a faulty gas cap. I know you said random, but does it happen daily or only after driven and warm or first thing and cold. How about light or heavy acceleration. Warm, cold, or rainy days.
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Sometimes using a real time scan tool will help isolate the problem, esp check the fuel trim parameters. If the fuel trim goes haywire in certain situations, like rpm or engine load, or only for certain banks, that can provide a clue.