Dana,
I'm sorry if this is out of line but I have to agree with the people telling you it doesn't sound like it's under control. Asthma that is under control does not interfere with a child's walking or running or playing sports and isn't triggered by exercise. Sometimes a child who has very severe asthma can't achieve that kind of control, but you don't want to stop trying after one mild preventative medication.
I don't mean to scare you but uncontrolled persistent asthma can cause permanent remodeling of a child's airways. My son has this because of frequent pneumonia as an infant and toddler and for the rest of his life he will have less lung power, less stamina than others his age, and will be more at risk of other lung related problems.
In my opinion, any child who is requiring daily asthma medication, or having symptoms daily needs to be seen by a specialist -- either a pediatric pulmonologist or a pediatric allergist. Pediatricians rarely know how to treat asthma the way it needs to be treated.
Again, I apologize if you feel this is out of line.
Emily