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Did you check or run a fuel pressure test while this problem has occurred? Does it continually maintain at least 30 psi on the fuel pressure? Have you checked for codes using the jumper wire in the diagnostic port under the hood and monitoring the flash pattern of the check engine light?
You cannot read codes on this with a code reader you have to use a jumper wire in the diagnostic port terminal connectors Te1 and E1 then turn the key to the on position and monitor the flash pattern of the check engine light. When it is in the no start condition or running poorly did you get a chance to check the fuel pressure? Can you use the jumper wire method and see what the flash pattern is on the check engine light? If it flashes steady and consistent there are no codes.