Take your daughter completely off ALL cow dairy--and I mean everything. She could have a casein or a whey protein allergy. If so, her body is building up pflegm and irritations in her lungs, and if she keeps eating dairy, her body isn't able to expel what it sees as a toxin and she's going to keep being ill.
For years, I was told that I have asthma, exercise-induced asthma, etc., etc. After my daughter was born, my asthma got so bad that I had to go on meds (Advair).
Fast forward to 2008. I turned 40 years old and became very sick. My doctor couldn't help me, so I turned to alternative healthcare. I discovered that I have an allergy to casein--I can't eat any cow dairy products (and you would be surprised how many products have some form of dairy in them!). After I went off eating all cow dairy--my asthma went away! I no longer have asthma, I'm no longer on asthma medicine, the rhinitis, sinunitis, chronic bronchitis, walking pneumonia, stuffy nose, wheezing, coughing, and all the other issues I used to have--completely and totally went away. Unless I inadvertently eat something with cow dairy in it--I no longer have any issues whatsoever with "asthma" or any other respiratory issues.
I would seriously try an elimination diet. She might be very, very allergic to cow dairy.