Do mutes persist between games?

Solution 1:

Yes, if you are muted by someone, you will be muted from their perspective when you meet again. It works the other way as well! If you mute someone during a game, they will be muted until you physically unmute them. It is persistent across all matches.

Solution 2:

They do in all of Valve's other multiplayer games, so I'm going to assume Yes until presented evidence otherwise.