sounds like either spark or fuel. did the dealership tell you that it is for sure a fuel problem? can you hear the fuel pump whine for a few seconds when the car is shut off and when you turn the key before trying to start it?
if it happens every time you turn off the vehicle you could test the coil, if it is good test a couple plugs. check for signal at the fuel pump. i dunno, if the mechanics can't seem to find the problem it probably won't be easy.