Engine just dying at a stop is hard to say, but likely problems are crank position sensor, or wiring harness; both will cause the symptoms you describe when first starting to go bad (be sure to check and or eliminate/replace these two things when related problems start occuring (irregular/rough running, loss of power, etc). Engine dying on cold-start could be system bleeding down, possibly due to a sticking injector pintle or fuel pump one-way valve with a fuel deposit on the ball valve. Hard to say past that.

__________________
Don't ask me, I'm a shop-owner by default