If it held its memory it would still idle fine. When you first start it after installing a new battery and it stalls right away the pcm has already reset. That is a first fire up precaution to protect a new engine at the factory. Trust me on this, after 40 years of being a Chrysler tech I know what I'm talking about.

You are having the warm idle issues because the pcm already lost its adaptive memory. You could just drive it for a week or so and it would eventually relearn but it would continue to stall at idle until it does. If it was a brand new engine with a clean throttle body then the second start would flare like a normal cold start and then idle down fine. But because the throttle body has carbon build up around the blades the pcm has no idea how much extra air to add with the idle air controller until it learns.