Typically, when I have seen this problem it was because the keyboard was not docked. It is deceiving because the keyboard can be up ever so slightly on the screen and it's not noticeable that it is not docked. So if docking the keyboard doesn't work, did you try turning the feature off completely.
Settings>General>Keyboard>Split Keyboard>Off.
IF that doesn't work, reset the iPad. Reset the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.
If that doesn't help, try this. Reset all settings. You will not lose any data, but most of the device settings will have to be entered in the settings app again. Settings>General>Reset>Reset all Settings.