i just used an SCT tune (93 octane, Performance tune) and a JLT cold air kit on and '06 GT and have had no problems so far with running or shut-off. i've read on the various 'stang forums that some cold air kits such as the
BBK don't require a tune the way other, larger diameter intakes do. may be that the tuner was programmed for a larger cold air intake. if that was the case, though, i would think the car would run lean and you would experience issues while driving. may be worth looking into though, all the same.