Over time fuel evaporation inside the fuel tank can lead to mild pressurization of the tank - that's why you hear a hiss when you first open the cap. It isn't much but that pressurization may be just enough to supplement a fuel pump that is only barely able to keep the engine running.
Quick test: park your car and let it cool for an hour or two. Open the gas cap and push the little secondary door that seals the top of the filler tube. Now there is no extra pressure in your fuel tank. Don't add fuel, just open the cap and door.
Now fire it up and see how it does. If it stumbles and hesitates, get your fuel pump checked.
It's possible there is a problem with the EVAP system. I had a similar issue when I did a custom engine swap, except mine didn't want to run when starting the engine immediately after filling up the tank.
In my case, I had the vent hose from the gas tank going directly into the engines intake, which flooded it with gas fumes from filling the tank up. There is suppose to be solenoid which controls when and how much of the gas fumes vent into the engine's intake, which I didn't have in my setup. I took that hose off the engine, and let it vent into the atmosphere, and that fixed my problem.
In your case, the solenoid, or something else in the EVAP system could be malfunctioning, allowing too much of those fumes into the engine at once, causing it to run rough or die.
Thanks Elhigh, I will do that test. Its a 2007 Dodge Caliber. Actually the car runs okay for 3-4 min after filling gas then starts shaking or stops. Then i have to start the car again and it drive okay until next time. It started happening 1-2 months ago.
Do you top the gas off, or just let it shut off by itself and stop? If you are topping off, stop it. If you aren't, I have no idea.
Is it a diesel?
