This is on a 2009 Chrysler Town and Country with a 4.0L engine (the one with the intake on top of everything)

About a week ago my wife's van started running really rough, had low power and poor fuel mileage. When I came home from work I took it for a test drive and found everything to be working fine. While on the test drive I stopped for a few minutes (I was airing up a low tire; for the sake of the story all that matters is I shut the car off). When I restarted the car it ran rough.

This led me down a guess and check path that yielded the following information-
1) it does not do it when the van is hot, only when it starts hot
2) the van runs fine when it starts cold, even when it gets up to operating temperature.
3) starting hot after the radio has shut off is where the issue is. If the van is shut off and the restarted before the power goes off, it has no problem.

I hooked up a scan tool and checked for codes and I got P0206 and P0306. 206 is a fault in the injector circuit for cylinder 6, and 306 is a misfire in cylinder 6.

So the question is, how confident are you that this is an injector fault? I've spoken to multiple shops/chrysler dealers and they all say that injector failure is very rare.

Mike