I know this is an old post but I am putting a new message here to help other cat owners with asthmatic cats.
Gizmo used to have frightening asthmatic attacks, but they were not consistent. The vet said that it was too expensive to put her on dilators when the attacks were intermittent.
She has not had a single attack since I got a BlueAir air filter for the studio (the dustiest room in the house and where Gizmo spends a significant amount of time.)
You need not get this particular brand, but a HEPA air filter will remove the dusts and molds that trigger an asthmatic attack. A HEPA vacuum cleaner is also essential. Other types of vacuums simply blast the dust into the air. Gizmo had her worst attack just after a cleaner vacuumed with the 'wrong' vacuum.
These machines are expensive but they will save you a fortune in veterinary bills.
In addition: They are good for
your lungs as well as for the cat's.