You could have a misfire, but every time you shut the engine down, the misfire counters for all the cylinders reset. You need to get a scanner that can provide live data and has a misfire counter for the cylinders. Perhaps the misfire counter never reaches the limit that it will throw a code since you say that the misfire is only at idle.

In order to solve the problem, you need to identify the problem. You don't even know which cylinder is stumbling or misfiring.

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