I've encountered this once or twice in the manner you are speaking, but I mostly encounter it when someone is either running multiple accounts or they just have bad internet. You'll wait a couple minutes between each round and the fight will take up to 15 minutes... Usually when it happens randomly in a fight between like only 1 of the rounds, it's usually that person dcing, but you said he didn't dc. The only similar thing I've seen to this is when I have 2 account open in the same mini client. If I have both accounts doing the same thing like TI/etc, The account that I'm not looking at will fall way behind so when I'm starting round 2, the game will just pause for a bit. I'll switch to the other account and it's only halfway through round 1. So maybe this is how the other person could have done it by switching to his other accounts tab while fighting you so that the account you're fighting loads slower, but don't quote me on that.