My daughter did this also. She would literally fall asleep after latching on! Then there was no waking her for more, two hours later she would be awake demanding another feed and the same thing would happen. All my midwife suggested was stripping her down to her nappy for feeding so she wasnt warm and comfy! I didnt like the idea of that but tried it anyway and she still went to sleep! lol Amazingly though she never lost weight.......even in the first few days to a week like babies normally do.
Im afraid after two weeks of no sleep and extremely sore boobs and nipples so painful I would wince and be in tears when she did feed......I gave in and put her on formula milk. I have to admit, it was the best thing I ever did! Almost immediatley she was on happily taking 4oz bottles and going 4 hours between feeds. Finally I was getting sleep!
Depsite all the problems, I will try breastfeeding again with the one on the way, hopefully it will be better this time. Sorry, no advice really other than if you feel like you cant do it anymore, like I couldnt, then change to formula as this may be the better option for baby and you.
Not sure if it has been mentioned, but just a thought, have you tried expressing and feeding baby with a bottle?