I feel for you! I haven't had asthma "all my life" - I developed it in my early 20s, and went through a couple of years of pain before getting set up with some maintenance meds that work for me. I'm by no means a competitive athlete, but I do enjoy participating in triathlons and running races (haven't quite gotten up the nerve to do bike races yet though!). I'm a pretty average middle-of-the-pack enthusiast.
Like you, I usually "run out of lungs" far before I run out of legs. Honestly though, I don't know if that's different from most people. Do you get actual attacks while racing, or do you just get that burning sensation where you just can't push it any more? I'm in the former camp, and I am definitely capable of decreasing my times by training. I would say that if you're not actually getting attacks during races then you're probably not that different from non-asthmatics... some people are limited by muscles, some by cardio.
TrainingProgram: I'm not sure what you mean by "keeping your body perfect", but asthma maintenance drugs are not illegal for games. My body is much more "perfect" when I inhale steroids and beta agonists every day than if I don't, so as much as I don't like being dependant on drugs, my quality of life is exponentially better when I'm taking them.