My idea on this (and I'm saying "idea" because I'm not a medical professional), is that wiht asthma, your production of mucous is greater and it can be more difficult to expel this mucous because of inflamed airways. Therefore, it tends to remain in the airways more and then when you start getting sick, it is already there for the bacteria or virus to set in.
I do agree with Liz about avoiding antibiotics if you can - the more you are on them, the more your body is going to become immune to them and then when you REALLY need them for a severe infection, they will be much less effective. Unfortunately, many times anbitiotics are prescribed too often for viral illnesses, for which they do nothing.
cargiver is also correct - if you are on steroids, whether they be inhaled, oral or injected, they will depress your immune system and make you much more susceptible to infections and other illnesses. If you need to be on steroids for your asthma, the lowest possible dose is the best way to go.
Since you've said your asthma seems to be allergy related, antibiotics definitely will not help. You need to determine exactly what it is that you are allergic to and avoid those items and/or be treating your allergies. If you do that, you may notice a decrease in your asthma systems and also the recurring infections.
My pulmonologist is encouraging me to request less antibiotics when I get a respiratory virus infection. If within a week, my peak flow numbers decrease and my body temperature moves from 97 to 98 or higher and I feel sicker despite a prescription for tapered prednisone, I want to be actually seen by a physician to prevent life-threatening illness. I like living.
Steroids, even in small doses, depress the immune system and increase the liklihood of infection. The infections are due to the use of a steroid to control the asthma.