I am also searching for a cause/cure for the same problem with my 5-yr old. He's had this non-stop burping issue for a couple of months now. First he had just gotten out of a cold and 9-day Antibiotic for ear infection, the doctor said his stomach was upset due to the Antibiotic (he was also frequently farting, stinky). He is recently burping continuosly, he happens to have a cold again, cough, phlegm, little apetite, slight asthma. I think (after what I have searched) this may have to do with gastrointestinal issue perhaps allergies, but I can't pinpoint what triggers it or how to help him. When he has a cold, I also stop dairy...
I will continue my search, I think I am taking him to the Allergy specialist this week.