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.