Wow, the silence on this one is deafening!

P, since no one has even attempted to answer this one AND you can't find anything similar to your issue by using search I think you may have just stumped the Forum!

Honestly, I cannot remember running across any thread that describes your problem BUT the first thing that pops in my head is still "battery".
My best suggestion is to buy another battery AND check to make sure your ground is tight & the battery terminals are clean.

We haven't had an above freezing day here since late November, if I remember correctly, and neither of our 2 Crossfires has ever hesitated starting or stopping right after they start.

Hey, something else just came to mind: try tossing a bottle or 2 of injector cleaner OR gas line anti-freeze (like Heet) in the tank. It's cheap & worth a shot.

Good luck!!!!!