Well, you can be sure that it isn't the fuel system, since the you've replaced every part that would cause the issue, and it probably isn't a sensor since no codes are popping up. I'm wondering if maybe you have a loose connection somewhere, a failing ECU, or a security system that is going crazy and shutting the car off. Come to think of it, what happens when the battery in the key goes bad?
Those were all guesses. If you take it to a tech, make sure you tell them about everything you've tested, and everything you've changed, so that they get a better idea about the issue and so that they don't charge extra for the time to check everything again.