Hi,welcome to Just Answer.I will be happy to assist you with this question today.I will try and assist you as best as possible from here,feel free to ask any follow up questions to my info provided here.
I just need a little more info to assist better.
Is it running rough when you shut it off after you have drove it then come back out and start it up?And does this rough running clear up after a few seconds in some cases?
Let me know so we can continue,thanks Pete.
o.k.,one common component to fail that can cause this fault here is the fuel pressure regulator.It will leak fuel into the vacuum line attached to it when you shut it off warmed up and then when you go to restart it the engine is partially flooded out and runs rough until the excess fuel is burned up.
You can check this by removing the vacuum line from it after the engine has ran and warmed up and check to see if any fuel is leaking out of the vacuum port,if there is fuel leaking out then it needs replaced.
It is located on your fuel injector rail under the hood on the drivers side.It will be the only component on the fuel injector rail that has a vacuum line attached to it.
It should look similar to the picture above.
It may be slightly different.
Hope this helps, and please remember to indicate that I have helped you today.
Place a rag under it if fuel does leak out so you can catch it.
Thank you.Have a great weekend and let me know if you need anything else in the future.