Do a search on lawn mower syndrome, you'll find plenty of posts on the subject.
The synptom does match carb. flooding. You would think going to ECU, this would go away but I've heard of occurances in other makes using ECU also. I think they may behave similarly but the source of the problem is different. There are lots of theory on why this is happening. Valve sticking, carbon build up, etc. Why cranking it for 2-3 minutes would eventually start the car is beyond me. There are no official service bullitin on it. I can only speak from my experience-3 times under very similar conditions. Fortunately, I was able to eventually start the car everytime.