Ugh, that poor baby. I hope the air purifies help, at the very least they will scrub the air in his room. You should leave it on 24/7. Some have quiet modes for bed time. Please make sure they are not ionizers sometimes called ozone makers, or if they have that setting that it is always turned off. You will know the ionizer is on because it gives off a strange odor.
Also be sure to vacuum the filters and the unit as needed, the more often the better. I have several pets and vacuum mine every 3-7 days. It's pretty loaded up if I let it go 7 days though. If he has carpet in his room, removing it would go a long way to getting rid of excess dust, pollen and dust mites. Also replacing pillows. If he has down pillows swap them out for non feather pillows. Does he have any pets in his room, like hamsters or guinea pigs etc.... do you have pets in the house?
They could be tracking in allergens, and if they spend a lot of time on his bed, that could be aggravating his lungs.
Has he had the different rounds of allergy testing? I did two levels, the first is that tiny prick they do on your arms. The next level is where you get higher doses in shot form. I discovered I am very allergic to ragweed, almost all hays (which my guinea pigs eat), highly allergic to dust mites and cockroaches.. among other assorted things. I am really glad to say we have never had roaches but I am sure we have dust mites like everyone else. Not fun, but maybe he needs to be tested at higher levels of allergy testing.
Poor guy I really hope you can find something that works for him and get it under control. I should also mention I have exercise induced asthma as well. But if he is the worst at night, doesn't sound like thats the issue. I feel like if it's allergy and its at night, something must bloom or release spores at night, or something is bringing it in. I have never looked into actual asthma, only allergy induced asthma so I can't speak to non allergy asthma. But if his mattress and pillow are not new (or even if they are) then cover his pillow and mattress with allergen covers:
http://www.amazon.com/s/ref=nb_sb_noss_1?url=search-alias=aps&field-keywords=allergen+mattress+cover
Wash all his bedding and see if that helps at all. Also what material is his blanket made of. He could be sensitive to fabrics like fleece, polyester or wool. I had to take my dog to an allergist and it turns out we are allergic to several of the same things. I mention it because when I brought her in the form asked what bedding she slept on and I realized her bedding is fleece (which is polyester) my couches are polyester, my couch covers which I thought were cotton are actually polyester too! You just never know what triggers it and it could just be too many of several things all piling up into enough to cause a reaction.
BTW, these are the anti allergen sprays and washes that I have been experimenting with.
They have 4 out of 5 stars on amazon:
This one doesn't have tannic acid:
http://www.amazon.com/ADMS-Anti-All...qid=1402966077&sr=8-1&keywords=allergen+spray
This one has tannic acid:
http://www.amazon.com/ADS-Anti-Alle...qid=1402965260&sr=8-5&keywords=allergen+spray
This is the laundry detergent:
http://www.amazon.com/Allergen-Wash...&qid=1402965320&sr=8-1&keywords=allergen+wash
If its allergies you might want to ask your allergist or the specialist if you should have an epi-pen in the house too.
OK thats all I can think of off the top of my head! Good luck!!