This really depends on the child.  After looking up some information I found that most babies are beginning to burp on their own anywhere from 4 to 9 months, with the majority being at around 6 months.

If you think that your baby is starting to burp on their own simply just stop trying.  If you notice that he/she starts spitting up more, or getting more gassy than normal, you may want to go back to burping your baby.

It may be that your baby is burping on their own, but if you don’t think he/she is but he/she is doing fine without you burping her/him, it may be that they are just swallowing less air while eating.