Help Battery Life on my S3

I am having some issues with my battery life on my phone, I am running a game (Empire Vs Orcs) and with power saving enabled, flight mode on everything else is off and screen brightness is on minimum, I have checked the battery via settings and nothing abnormal there, the phone has not been reset in about 24hrs. But whilst charging with the suppied charger via a mains output, the battery life is slowly decreasing by about 1% every 5 mins. When I do a fresh restart it holds the battery at 100%. Is there a way I can keep it like this without restarting the device?

Also I heard mixed things about replacement high capacity batteries found on ebay etc. Is there any batteries which will extend the life and no require changing the dimension on the phone?

Thanks forthe help