I don't, to my knowledge have asthma, but this summer I had pneumonia (second time in life). I was down, literally for 8 weeks. I couldn't walk from my home office to the kitchen without feeling like I was going down.
I used the albuteroll and inhaled steriod several times a day. When I thought I was getting better, I started to ride again and getting back into the saddle was very slow. I am now back to riding 25-35 rides in the hills. There was a time I wondered if I would ever get back. I think you have to listen to your body and only go until you sense the need to shut down.
Good luck to you. Some may disagree, but you can not fool your "real" health. I understand how disheartening it would be if could not ride anymore, but I would choose physical stability over my desire to do what I enjoy. I would just find a replacement within my ability.
Good luck to you.
Jay