Hi! There are many possible causes, but he surely needs to see a doctor & get a thorough check up. It be allergies, stubborn infection, or other causes, but since it's persisted for a month, he should be checked out.
It may help if he diaries when the shortness of breath is worse & when it improves (if ever). His regular family physician would be a good place to start. He can be referred as needed afterwards.
Trying to guess why he is having shortness of breath would not be productive without more information.
Aloha,
Starion
Shortness of breath and an unproductive cough could be due to a lung or heart problem. Other possible causes are allergy, infection, irritation or all of these. Many viral infections, most notably the flu, can cause irritation of the airways of the lungs. This irritation can cause a cough that lasts for 3 to 6 months. In a person who has a normal chest x-ray and who doesn