As far as I know, there is no way to save the game for a break. If you do, it converts to regular PBEM and will not upload back to the server and you then have to email the game to your opponent (I could be wrong ... if there is a way to do that, chime in). For me, in the large scenes, then I just leave the game running if I need a break. I've left it running for hours while running errands etc., never had a problem w/ it (yet LoL) ...
When you finish the move (when the final combat resolves, or you end your turn) then the machine will automatically load your reply to the server. I hope this helps! Someone correct me if this is wrong, I too would like to have ability to "save" a game mid-turn in the server style, esp. useful for FitE2 or similar huge scenario.