Your doctor is wise.  Advair is a medicine that works so well to control asthma that it may actually prevent your exercise induced asthma (EIA) from occuring.  Most asthma experts now believe that EIA should be treated as any other type of asthma.  Since you are having asthma symptoms while running, chances are you have some underlying (chronic) inflammation in your lungs that is only aggrivated when you run, thus causing your asthma symptoms.  If you treat this underlying inflammation, you may be able to exercise without asthma symptoms.  Advair is a great medicine to not only treat this underlying inflammation, but prevent any bronchoconstriction (airway narrowing) that might occur when you exercise.  You may also learn that after being on Advair a while you may not even need to use your Maxair anymore.  But, as always, whatever you decide to do please talk with your doctor first. 

On a side note here, I can tell you from personal experience that Advair works great.  I use it to control my asthma, and I am now able to exercise without my asthma flairing up (most of the time).  My advice to you is try it and see what happens.  You may really like the results.