I really could be anything between you and chess.com. It is really hard to say.
CHESS.COM's connection interrupted bug
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It could be any number of things. You should disable Flash for this site, if you didn't have that done already. Also, take a look at the following as it can provide some suggestions.
https://support.chess.com/customer/en/portal/articles/1444918-my-internet-connection-is-fine---why-am-i-getting-disconnects-
It could also be an issue on any of the hops your conmection goes through to get to the chess.com Live servers.