Personally, I managed to beat Razor (finally) by having him get stuck on top of one of the poles in the corners. Just heavy punched him over and over and he wouldn't attack back. Weird glitch.
At this moment the fistfights got completely broken because blocking and counterpunching will result in me receiving FULL damage, I block a punch i get full damage, I counter a punch I get FULL damage. The first fight with the twins was OK, except I had no sound when I was getting punched but I could at least block and counter.
Then after I played 40 hours of main game with story missions and side quests etc, I resumed the quest and at the fight with the black guy named Brock or sth this problem just appeared and it just wouldn't fix itself by reloading multiple saves or restarting the game. I could beat them all (the 3 other fighters before Razor) by running away and spamming heavy hit but I cannot beat Razor because there isn't any fucking room in the boxing ring to use my only available resource to finish this fucking quest as i can't finish it on easy because he somehow still needs 50000 hits to be beat on easy. and usually once he hits, he hits, and there's nothing I can do about it. I always run out of stamina to keep staggering him, and even if I could still win using this, it's completely unfun and pointless.
Sorry for the language but this was a beyond infuriating experience and it feels satisfying to express it like this
It happened to me as well. My explanation is that the game, to determine if the attack succeeds, uses the player's position about halfway through the attack animation. After I started to move away earlier, sometimes even anticipating the NPC, I was fine.This is exactly what I ran into. I'd literally be staring at the opponent (from a side-view) kicking air as I take damage. Not sure if it's fixed now, but I'm still going to wait a while (for possible patches) before trying these quests again.