How can I avoid timing out when the site won't save my turns?

I'm winning a casual game on turn 27, but now there's 3 hours to go in the turn and the stupid site won't save my turn. It says it will, but it keeps losing connection, and after I save my turn, trying to return to the lobby does not work. Reloading the site reveals my turn was not actually saved. I'm about to time out.

Anyone experienced this? Any advice on how to deal with it?