After fueling my '04 Sonata it is hard to start. It seems to have lost fuel pressure. I noticed that if I remove the fuel cap when the engine is running it will die.

 

I heard a similar story on ‘Car Talk’ some weeks ago. The problem was caused by filling the tank to the top, beyond the automatic cutoff of the gas pump. The additional gas affects a valve that causes the difficult starts. They (Bob& Ray) recommended the car be taken to a garage (dealer?) that has a device to clear this valve. It is a common problem. I recently did some work on my gas tank and removing the gas cap is one step in the process to depressurize the fuel lines and would likely cause the stall.

 

Six year old vehicle 'prolly due for a fuel filter change.