Allergy Shots & IGA deficiency

My 4 year old son has a borderline IGA deficiency (IGA was 15 and 20 on two tests - normal for his age is 25-160) .  He gets a bronchial infection/sinus infection once a month.   Because of his low IGA, he needs 20+ days of an antibiotic to clear the infection.  7-10 days after completing the antibiotic, his nose starts running, he starts coughing and within a day he has a full blown bronchial infection again.  My question is could his monthly allergy shots be triggering his infections?  His pediatrician, allergist and immunologist say to not stop the allergy shots since we have finally progressed to the once a month shot....but I am desperately trying to understand how he can get sick every single month!!  Anyone out there experiencing a similar situation??  HELP!!!!!!!!!!!