It's going to be pretty hard to pin down if it doesn't set a diagnostic code. Most electrical or electronic failures should. You might even be able to test this theory by disconnecting suspect devices and seeing if they do throw a code. I don't know on a 99 whether or not all codes will set the check engine light, but it might be worthwhile getting an OBDII reader on yours to see if there's anything there.
If possible, you should find out if when it dies, you have a spark. This would help narrow things down. Many electronic components can fail when they get hot, and so can some wiring junctions, and it can be very difficult to track down. The coil is certainly one possibility but it isn't the only one.