The constant reloading was happening to me also about 4 days ago , but with online / turned based games. I would make a move and it would just constantly reload. The only way to make it stop was to power the ipad down even if I closed out of the app and came back it would still be loading the move. It is working properly now.
Just curious, when your playing live games are you playing strictly through the app or do you go to the site from the app using safari?
Lately I've been having problems on live chess with ipad disconnecting then reloading constantly. Usually I run out of time while waiting for my opponent to move. It makes live chess unusable. I'm assuming its on my end tho my ISP speed is respectable. This is only on chess.com. I play on another site and it's just fine. Tried re downloading chess.com app but still does the same. Any ideas?