Check out the info in this thread.
It will give you the short version of my suspected eventual diagnosis, and a long version of my horrid ordeal with the POS.
My best advice would be to try the following:
Don't fill you gas tank for a few weeks, stop a few gallons short of full basically, and see if it goes away. We drove our Jeep for something like 2-3 months like this while we waited for the lawsuit to settle, and it never stalled once. Filled the tank to where the pump shutoff just once by accident, started stalling again randomly for the next few hundred miles.
Had I not been out of patience with the thing by then, I would have pursued having the gas tank replaced - but by then it was game over for me and Jeep.
Best of luck to you all with this same problem - I hope you find the diagnosis steps provided help narrow down the culprit. Do us all a favor if it works, whether or not you pay a dealership to fix the issue, please go in and tell your dealership that these codes and this problem were related to the gas tank. Drop a letter to someone technical at Chysler and let them know as well. Strange problems exist everywhere, but all I'm saying is it is a damn shame that the ONLY resolution I found to this problem came from a former Chrysler engineer hanging out on a GM forum I'm on after ditching the other Chrysler in my fleet for a GMC and mentioning the problem somehow. If it wasn't for that guy, this miserable problem would still haunt my mind despite it being over a year since I dumped my Jeep.
And while it's definitely not brand bashing, I personally like the products offered by Chrysler, but my opinion is if you're not going to sell a quality product you should at least take the time to make sure all of your highly skilled techs are aware of the faults of your vehicles. Please, don't take that as a knock to a single tech or engineer working on these vehicles post sale, but simply as in addition to my frustration, I saw the frustration on the faces of the guys who tried their best to fix my Jeep and if you're a mechanic of any sort, you know how if feels when you have to "give up" and no one was happy in this ordeal.
And again, not to brand bash, but I've found the grass is sometimes greener on the other side. Ditched a Ram for a GMC and have 25k miles without a hint of a reason to make the drive back to the service department where I bought it from worth the free oil change it came with. Ditched the Jeep for a VW (definitely an apples to oranges comparison - it's job is to get the wife to work in the snow which it does, but doesn't haul the boat like the Jeep did) and 18k so far without a single complaint or issue yet. If you tallied up the number of visits each Chrysler vehicle before it had at the same mileage, you'd do what I did - never look back.
Best of luck to everyone - if you don't mind, I'd like to hear whether your problem was the same source as mine and how it gets resolved so keep the thread going please.