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Hi Jenni, I'm not sure if this is a game problem or a Facebook problem (it started happening after facebooks recent update!) but there is a way to stop it happening so much.
When you are playing Pet Rescue (or any other facebook game this happens in) do not open any other thing on facebook (game, message, group post, notification etc) while you are in the game. Only have one tab/window open with the game.
If you do open anything else on facebook, you will not see the disconnect message immediately, but it pops up the next time the game tries to save or connect (for example at the end of a level)
This will not eliminate the disconnection message problem, but seems to make it happen less.