If rinsing and gargling do not help. Be sure to get your thyroid checked. Having one autoimmune problem (asthma) puts a person at risk for others-- in this hashimotos (autoimmune thyroid). I see that you are near Chicago if I r Dr. Paloyan is an excellent thyroid doctor. If you can see him make an appointment quickly, I have heard his appointments fills up quickly.
Edward Paloyan MD and Associates
333 Chestnut St Suite L03
Hinsdale, IL 60521
(630) 655-0722 (Office)
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mklarson provided an excellent suggestion regarding a possibility. That rinse and gargle is extremely important.
Can asthma cause this? possibly...more than likely it is the Advair. I little known fact about Advair is that only ~16% makes it to the lungs where you want it. The rest of it sits in your mouth and throat, therefore, it is very important to rinse and gargle after each use. The drug which is good in the lungs, is bad in the mouth and throat. It can cause fungal infections, hoarseness, and temporary loss of voice. You may need to have a throat culture done to make sure you do not have a fungal infection. I am not saying that this is the only possible reason you have problems losing your voice, but I would put it at or close to the top of the list.
Hope this helps!