I recently got the iPad app and today I tried playing my first online game. It was a disaster - nearly every few minutes, I was interrupted with a "network connection lost" popup, then booted out to the lobby screen and forced to reconnect and sit through the loading screen. I would get this popup even when nothing was going on and it was my turn and I was just pondering my next move. Of course this makes it almost impossible to focus on the game if you're getting kicked out every few minutes.
Given that this is a turn-based game, I have no idea why losing connection with the server would require booting the player out entirely from the game. Can't you just flash some icon or something and prevent the turn from being submitted until connection is re-established? This is literally game-breaking and means I can only play offline.
I was playing on my home wifi connection and have never had any issues with it or other online games.