Why my ipad keeps shutting down

First try a Reset ( No Data will be Lost )

Press and hold the Sleep/Wake button and the Home button at the same time for at least Ten seconds... (But can take Longer)... until the Apple logo appears. Release the Buttons

If no joy... Try a Restore...

1: Connect the device to Your computer and open iTunes.

2: If the device appears in iTunes, select and click Restore on the Summary pane.

Restoring > http://support.apple.com/kb/HT1414

3: If the device doesn't appear in iTunes, try using the Steps in this article to force the device into Recovery Mode.

Make sure you have the Current Version of iTunes Installed on your computer

iTunes free download from www.itunes.com/download

Note on Recovery Mode.

You may need to try this More than Once... Be sure to Follow ALL the Steps...

After you have Recovered your Device...

Re-Sync your Content or Restore from the most Recent Backup...

Restore from Backup > http://support.apple.com/kb/ht1766

Direct renew with Apple customer service.