I had the same problem with a 1996 Dodge Avenger 4-cylinder manual transmission and found out that is was the Idle Air Control Motor is located right underneath the Throttle position sensor. It will run as long as a revved the engine but as soon as I would let go of the gas pedal it would not idle and it would shut-off.
my 1992 dodge dakota wont stay running it stalls when driving and takes a few minutes to get started but if i wait it will start
You could have air bubbles in your gas line.
Dodge Avenger has a problem with this. You need to take off the oil pan because the oil thicken's in the pan. Clean it and put it back on and this should to the trick.
worn out tierods
It is very easy to check the transmission fluid level in a 1995 Dodge Avenger ES. You will need to park the car on level ground and keep it running while checking the fluid level. The dipstick is located where you put the transmission fluid.
check the vaccums lines like the PVC valve to see if the hoses are cracked and need to be replaced or not.
Check your belt tensioner idler pulley, I replaced mine for about $120.00 from a Mitsubishi dealer compared to $170.00 from a Dodge dealer. 1995-2000 Dodge Avengers were made by Mistubishi for Dodge.
Check your hood alignment sensor for the alarm and the trunk sensor
Why engine stalls on 1993 Chrysler Intrepid while driving and sometimes at stops?
if cutting in and out while still power in car may be engine computer or computer wiring. if all power cutting out then its possible car battery cables.
have the cam position sensor checked Check fuel pressure.
PCV stands for Positive Crankcase Ventilation, is a valve that releases air by turbulance created inside the engine when the crankshaft and piston are turning while engine is running.