Does he take these 'deep breaths' only during exertion of some kind or all through the day?
Please take him to a pediatrician
as soon as possible & establish a diagnosis.
It could be any of the following reasons:
a) Nasal obstruction/ allergic swelling of the nasal mucosa.
C) Iron deficiency
d) Cardiac causes
e) Renal causes
All the best & take care