Are you breastfeeding? If so, yes, it can be pretty typical at his age to keep falling asleep....I know it's frustrating hey!! My DS was a sleepy baby too and would take as long as an 1hr-1.5hr to nurse. It too started to affect his sleep since by the time I changed him after feeding, put him to bed, he would only be sleeping for maybe an hour before his need feed was due. I tried all the things you did and nothing ever really worked, maybe try burping or walking your fingers down his spine.
The reason he is falling asleep could be due to a couple things.....when you breast feed, you release oxytocin causing babies to become sleepy.
Maybe your let down is too slow and he is getting bored and falling asleep. Unfortunately, you can't really control either situation if these are the causes.
I ended up stopping BF and going to the bottle (for other reasons). Things dramatically improved...