I definitely agree with taking your baby for another opinion. I would also have him seen by an Integration doctor (this is a medical doctor who also holds a degree in naturopathic/alternative medicine). This type of doctor will look for heavy metals (they can cause allergies, asthma, and a host of other problems) and also food sensitivies/intolerances. Is your baby still on formula/breast, or is he eating solids? The baby can be intolerant of foods, even if he's only getting them through breast milk. If he's on formula, especially soy, that needs to be checked as well. Soy is a very big intolerance food (a saliva test can test for the 4 most common food intolerances: soy, dairy (casein), egg, wheat (gliadin).
One thing I would do right away is get your little one on a good pediatric probiotic (a community pharmacy can help you with this). Because he's been on so many antibiotics, his system is screwed up, including his digestive system. Adding probiotics/the "good" bacteria will help his system start healing and reregulating itself. Another thing you'll want to be careful and check for is leaky gut; an Integration doctor can help with that. Also, since he's been so sick, his minerals and such might be off; the Integration doctor can check for that as well.
Why do I say go see an Integration doctor? Because the advice I've given above, the different areas to check, is information that normal conventional doctors are not privy to. There are two things regular doctors are not taught in medical school: 1) anything having to do with nutrition and 2) heavy metals (this includes environmental, pesticides, herbicides, etc.)
I agree with another poster, there is more going on here than just asthma. If I were to wager a guess, I'd say he has some underlying problem the doctors are not finding. If they've "done all the tests" and everything has come back "normal"--then it's time to see the Integration doctor, because she will take different tests that the conventional doctors don't believe in. (Believe me; I'm currently seeing an Integration doctor myself for heavy metals, food intolerances, and what might be a mineral or hormone problem).
Good luck finding relief for your baby and help for yourself. Please, let us know how things turn out.