This battle isn't about breastfeeding, it's about sleeping. It's a really tough one. The best thing when youfind yourself in this sort of spot is to stop.
There's nothing wrong with your baby, or with you either for that matter. It may be that he's ready to drop a sleep (how many is he having) or to go to sleep a different way. If he's putting up a fight, then put him down. If he still wants milk, then fine, but make it about feeding ,not sleeping. Then stick him in a pram and go for a walk or do something else completely different.
When DS was like this I started walking him to sleep during the day - still do sometimes. I'd sit him up with a bickie (so there was no suggestion that I expected him to sleep), and he'd nod off pretty quickly if he was tired enough. Had to take him unawares.
Don't fight on, trying to get him to sleep if it's like this - it's horrible and depressing! I know he's crazy tired and desperately needs to sleep, but it really isn't worth it.