The chat is actually not flash related - it has a mechanism that contacts the chat server every minute to check that you are still alive. If you miss those checks, the chat server marks you as 'dead' and disconnects you. You are reconnected once your client starts responding again.

When your MacBook (well, this is true for every computer not only Mac) goes to sleep, it stops responding, and the chat server disconnects you eventually.
If you resume playing, the chat should come back online after a minute or so (Optionally, if you want the chat immediately, you can restart the game).

• Edited on 22/07/15