I'm certainly no asthma expert but I wouldn't figure exercise induced asthma would go away if you continued running at the same pace after a couple of miles.
Here's a site with some good basic info on it:
http://www.emedicinehealth.com/exercise-induced_asthma/article_em.htmIf your pace stays the same, the breathless feeling happens but then fades at the same pace, it almost sounds like you're getting the proverbial "second wind". I'd read somewhere that was a sign that your body had warmed up and gotten more efficient; settled in, so to speak.
I guess I'd look at tracking when it occurred for a while....look at environmental factors like heat/cold, humidity, environmental pollutants, etc. Time/distance until it occurs and then until it ceases. Pace fluctuations. Anything to see if there's a pattern that might help zero in on a cause, or at least a set of triggers.
Then, armed with that info, you might want to consider getting tested so you'd know for sure.