When you say "has asthma listed several times", does that mean it's in his records as a diagnosis? If so, and if you checked the box on any of the asthma related questions, then you will likely be asked to provide remedials. There is a specific asthma remedial form they ask you to complete, and provide all the medical records related to it.
Unfortunately, if the word asthma exists anywhere in your records, it's almost automatically a DQ.
However, it is very possible to get a waiver for asthma after age 13. You will need to be proactive.
My DS had an asthma DQ, even though he submitted records from a pulmonologist that definitively stated "does not have asthma" and also included a negative Methacholine challenge test result. What I was told by DODMERB is that, "the record indicates a history of asthma, and even though the doctor and test results indicate otherwise, the waiver authority will need to review" Basically, they do not exercise any discretion, and will defer to the SA/ROTC for waiver decision.
DS eventually received a waiver from USNA, but it took quite a while. If you haven't already, you might want to look into getting a MCCT done. We got it done and insurance paid for it. We also printed out the relative section from DOD 6130.03 and showed it to the pulmonologist so that he could make sure his evaluation addressed the qualification standard very clearly. Also, be sure to read and understand DOD 6103.03, so you can be sure that any documentation that you submit isn't going to create any new problems.
good luck!