Figure out which key starts the jeep, with the engine off but the ignition in the run position press the lock & then unlock on the key.
This preforms a hand shake with the system that hopefully solves your issue.
It works with keys that open the locks but engine keeps shutting down because the key is not recognised.
Even though your problem is different hopefully it resolves your issue.
If I could live with the fuel bill (& fines) I would love a HEMI