Ipad, 3rd generation, not updating apps automatically

As an initial step, which may resolve the problem - is to disable automatic update of Apps in iPad settings, return to the Settings top-level, the exit/close settings. Next, force-restart the iPad:

• On an iPad with a Home button: Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.
• On other iPad models: Press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the top button. When the Apple logo appears, release the button.

After restarting the iPad, you can re-enable auto-update in Settings.

Please clarify; are you having difficulties with auto-update of Apps already installed on your iPad - or with your System Software Updates?

Assuming that you are having difficulties with automatic update of Apps already installed, ensure that Automatic Downloads are enabled in Settings (shown here disabled):