I happened to be listening to the car guys on NPR and this issue on another model came up. The best guess they had was a diaphragm in the carburetor. Example search.
https://www.google.com/search?q=carberauter&ie=utf-8&oe=utf-8#q=carburetor+diagram+stalling
Let me be clear, same symptoms of stalling, rough idle and sometimes turning on the AC can cause it to get by.
Hope this helps.
PS. https://www.google.com/search?q=2000+Dodge+neon&ie=utf-8&oe=utf-8#q=2000+dodge+neon+idles+rough finds you're not the first to notice this issue/problem.
Hello forum members!
I have a 2000 Dodge Neon with a 2.0 liter engine/ 16 valves and manual transmission. The problem started about two months ago when it simply turned off with no prior notice (no jerking etc.) while at a stop light. I am able to turn it on as soon as it turns off and it turns on just fine with no problem whatsoever. When it does turn off (it happens maybe twice a week at seemingly random times) I did notice the last few times that the idling was just a bit rough, nothing too significant and that right before turning off the rpms would start dropping until it shuts off. This has happened with the clutch disengaged and the gear on neutral. Dont know if its my imagination but I think that if I rev the car up a bit while in neutral it keeps the car from shutting off whenever I "sense" that it's about to turn off. I had the crankshaft sensor replaced about a year ago and that's about it. Got the spark plugs changed too but this was about 3 months ago. Im not too savvy with car tech problems but i get the feeling that this may be a problem with some sort of a sensor or fuse or something electrical. My gas mileage with the car hasnt changed and my car drives fine other than that. This problem has never happened while driving. Got the car scanned and no codes came up either. This only seems to happen when my car is at normal temperatures (not when its cold) and it doesnt overheat. Any thoughts on this? Any help on the matter would be greatly appreciated. Thanks a bunch!

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic