2005 Dodge Durango stalling, sporadic idling

If this only happens at an idle, have you checked for vacuum leaks? Have you checked the idle air control valve (IAC)? The IAC is responsible for maintaining the engine's idle speed.

2005 Dodge Durango: had a rebuilt transmission, put in about a year ago, replaced spark plugs. A year later. As I slow down to stop. It stalls out. I have had BG automatic, look into this. First issue, was I needed a new key, the old one had a programming issue. Then it keeps doing intermittently, from one week to maybe three weeks apart. They have been great at keeping vehicle, but it has not did it to them. I looking for a reliable place in northern Colorado, to take my vehicle too.

This is common when you have a vacuum leak, or the throttle body needs to be serviced.

These guides should help you fix it:

https://www.2carpros.com/articles/stall-at-idle

Follow this guide when the engine is cold:

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

This one you should do as a service anyway so it can't hurt:

https://www.2carpros.com/articles/throttle-actuator-service

Please go over these guides and report back.