When you click the Turn on Automatic Updates button in the Windows Security center applet, the following error message may appear:
We're sorry. The Security Center could not change your Automatic Updates settings. To try changing the settings yourself, go to System in Control Panel. On the Automatic Updates tab, select Automatic (recommended), and then click OK.

This happens if one of the following services are not started:
Another possibility is that the Automatic Update Policies might be enabled.
Download the vbscript available at the bottom of this page and save to Desktop. Double-click to run the file. The script enables both the above services, and removes the Automatic Update restrictions automatically.