You referring to the website? I play on the mobile app and it always stays disabled.
Disabling Chat
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Playing on iPad.
Dec 29, 2015
0
#4
I'm pretty sure that if you disable it after the start of the game, it only stays disabled for that game.
If you want to automatically disable it for all Live Chess games, you need to update it in your settings at http://www.chess.com/home/livechess_settings
If you want to have chat enabled by default and just want to automatically disable it for that particular opponent, then I think you're going to need to request that as a new feature...
I notice that when you disable chat, it does not stay disabled if you accept a rematch. I think it should.