I'm having exactly the same problem with my '99 GT. It started last summer and happened pretty randomly until winter. For whatever reason it didn't happen at all this winter. Just today it finally did it again.
In addition to this, I'm having another problem that I think is related. I'll go to start the engine, and it will crank and crank, but not fire. After multiple attempts and a few minutes later, it will just all of a sudden pop right off when you hit the key and idle perfectly like nothing was wrong. If you just let it sit for several minutes, the same it will start too. The reason I feel these problems are related are that they started happening at the same time, and they appear to both be electrical issues affecting ignition.
I have had the car into a couple mechanics, but like you said - there are no codes in the system and everything checks out. I think it would have to act up with the diagnostic equipment hooked up to see anything.
So, unfortunately, I don't have a solution, but I'm as interested as you are in what it could be.
One thing that was suggested to me that I haven't tried yet is to swap out relays in the fuse panel under the hood. Is there any possibility that a relay could be causing these problems in the ignition circuit?
Eric.
