Thank you for your inquiry.
Actually, the question that should be asked is not "Can" but rather "May" a patient with persistent asthma be a fireman". To help you understand the distinction between the two phrases, I have copied below the websites of various governmental organization statements regarding the health requirements of firemen in their locales. If you click on "find" and type in "asthma" into the search box, you will be able to pull up each individual site's recommendation.
What you will learn is that asthma is not an automatic exclusion from this occupation, but an exclusion based upon different criteria in different areas. It is a requirement, however, that a person with known asthma be evaluated (usually by a specialist in the area; most commonly mentioned are pulmonologists) to clear participation if the physician feels it is indicated. In my personal experience, I have permitted asthmatics with normal lung functions or only slightly lowered FEV1 values to be firemen, pending meeting other local regulations.
So what I would suggest is that you glance through these PDF documents to get a "flavor" for the types of limitations that exist, and if you are personally responsible to assist in making this decision, obtain the local regulations from your fire department, evaluate the patient, and make a decision within their prescribed boundaries.
Thank you again for your inquiry and we hope this response is helpful to you.
Revision Date July 26, 2012
Firefighter Applicant Instruction Sheet
Asthma Medical Form
(For respiratory conditions other than asthma, please complete the “Other Health Condition Medical Form”)
South Dakota Department of Labor and Regulation Divistion of Labor and Management
Comprehensive Occupational Medical Program for Fire Departments - Orange County
Phil Lieberman, M.D.