Okay, I looked it up. It is a corticosteroid. Not quite the same as a steroid (like prednisone). It is very similar to Advair, just a different corticosteriod. It's kind of like all the allergy nasal sprays--Flonase, Rhinocort, Nasonex. They all are essentially the same, just a tiny bit different.
Anyway, Asmanex and other drugs like it are meant to be used in the long-term management of asthma. They should be used every day as a preventive measure so that you DON'T ever have to use the albuterol inhaler. Too much use of the albuterol can make bronchial tubes "brittle." Stick with the Asmanex, it is probably going to keep you off all the other medications.