Burping a sleeping baby - help!

Does anyone have any advice on how get a sleeping baby to burp??

Now that we are waking up multiple times during the night for feeds

my baby will often fall asleep while eating.

I consistently burp him throughout the feed and have no problems but once he completely zonks out - I cannot seem to be able to get that last burp up!!

I try multiple burping positions (over knee, sitting up, over shoulder) but it almost seems impossible. So then I try to hold up upright for as long as I can without falling asleep myself and put him down only for him to awaken 5,10,20 mins later with a burp.

Anyone else have this problem? And what do you do??