Are you a nurse? Can you check her pulse and respiratory rates during an attack? Can you listen to her lungs with a stethoscope? What happens before the attack? And how does the attack end? (I mean, can you calm her breathing by talking with her or does having the air conditioner in the car on help, whatever...)
I'm certainly not a doc, but it's been my experience that acute asthma attacks don't end spontaneously - they usually need some kind of intervention with medications (by nebulizer or whatever). Other things can cause difficulty breathing, and having some kind of physical obstruction could certainly be one. Does some sort of activity or movement start this all off?
Does this seem to be related to any food, medication, contact with anything (the cat or dog, chemicals, feather bed, whatever...)?
I forgot how old your daughter is, but is she in puberty? Those pesky hormones can sometimes cause anxiety leading to hyperventilation. So can anxiety about other things (school, boys, friends...). Could she be anemic?
I would advise you to stay as calm as possible when these occur while trying to observe as much as you can (make a note so you can remember the specifics to tell the doc). Don't hesitate to go the the ER or call 911 if she is in acute distress.
Here's a great pediatric site: http://www.med.umich.edu/1libr/pa/pa_index.htm