I keep getting kicked out of games.

What have you tried to fix it ? Have you tried closing all apps via the iPad's taskbar and then doing a soft-reset and seeing if that makes any difference ?

To close all apps, double-click the home button to open the taskbar, and then press and hold any of the apps on the taskbar for a couple of seconds or so until they start shaking, then press the '-' in the top left of each app to close them, and touch any part of the screen above the taskbar so as to stop the shaking and close the taskbar. (With iOS 7 you swipe or drag an app's screen from the taskbar up and off the top of the screen to close it.)

A soft-reset : press and hold both the sleep and home buttons for about 10 to 15 seconds (ignore the red slider), after which the Apple logo should appear - you won't lose any content, it's the iPad equivalent of a reboot.