'05 ST stalls once a day

My 2005 ST has 67,000 miles on it (I commute 110 a day round trip), and it's developed an interesting starting problem. Goes in streaks, unfortunately, so the mechanic has only been able to reproduce the issue once two weeks ago, and he decided it needed a new fuel pump which obviously wasn't the problem because it's back. The problem: first time I start it in the morning it cranks strongly, starts up, then stalls immediately. Usually I can start it easily on the second try and it keeps running. Other times, it cranks for ten seconds without starting until I depress the gas pedal about halfway. When I start it after work (it's been sitting outside for nine + hours), it's always fine, no matter what the weather. It's in an unheated garage all night, but the temperature doesn't seem to be a factor anyway.

I took it back to the mechanic two days ago, and he said there was a service bulletin from Ford about needing to recalibrate the PCM, which they did this time. I've only started it once since I picked it up, and it started fine, but I have serious doubts that it's going to stay that way considering the previous fixes they suggested, so I'm coming to the REAL experts here at the forum for suggestions.