Starts when cold but stalls and won't idle

[patarusky]

So my focus just started to do this thing where it starts right up when cold but dies right away. I can restart but it won't stay idling. So I tried to feather the throttle a little bit to keep it running and that works. After about 20 seconds I can take my foot off the throttle & it runs and idles fine. In fact ,the rest of the day it starts & runs great with no idle issues. But after it sits overnight the issue comes back. So here's what I have done so far:I found that the valve cover gasket and the 4 spark plug gaskets were letting oil down on to the plugs so much they were fouling out. Bingo! I thought. So I changed all the gaskets and installed all new plugs. It runs better but that did not solve the problem. Next I looked at everything under the hood for anything out of place. Of course there is no check engine light on. Next I borrowed a high end scan tool and ran some tests. Here's what I found on the scan: All o2 sensors are working fine. Fuel pump pressure is steady at 40 psi on the fuel rail. Egr valve is working fine. Purge valve is responding and working fine. Short fuel trim & long fuel trims are working fine. MAF sensor is working fine. So now I need some input here.1st cold start no idle. then rest of the day starts & runs perfect. Next morning no idle again.Help.