Need Help with Windows Update Error Code 80072EFD!

Twiggy,

In addition to what others have (rightly) said,

Is the system's time, date and year set correctly ?

 A rootkit has been known to cause this issue.
Update server closing the connection.

(Rootkit Removal tool Tdsskiller)
http://support.kaspersky.com/viruses/solutions?qid=208280684
Also, suggest that you scan your computer using MalwareBytes' to remove any traces that may still be present.
MalwareBytes Anti-Malware (MBAM)
<http://www.malwarebytes.com/>
The free version of MBAM is an on-demand scanner and offer no 'real-time' protection. Keep installed and use it as 'second-opinion' scanner.

You can  reset  Windows Update components by running the Fixit on this page.  But, if there's malware present, it will continue to reset the connection to the update servers:

How do I  reset  Windows Update components
 <http://support.microsoft.com/kb/971058>
Suggest you download and save the Fixit.  Then configure the system to Clean boot prior to running it:

How to troubleshoot a problem by performing a clean boot in Windows Vista/Windows 7
<http://support.microsoft.com/kb/929135>

Once the Fixit has been downloaded and the system booted to the Clean state, check to see that the native Vista firewall is now On if a 3rd party firewall was being used previously.  Now run the Fixit and choose the Default mode.  Restart once it's done and see if the system can connect to the update servers.  If it can not, then run the Fixit again and choose the Aggressive mode.  Restart when it's finished running and check for updates.

Windows Update error 80072efd
http://windows.microsoft.com/en-US/windows7/Windows-Update-error-80072efd

If you receive Windows Update error 80072efd while checking for updates, the cause might be a connection interruption between your computer and theWindows Update servers. Close Windows Update, wait 10 to 15 minutes, and then runWindows Update again. You can also wait for Windows Automatic Update to run at its next scheduled time.

Windows provides a built-in troubleshooter that can automatically find and fix some common problems withWindows Update.

If you continue to receive this error, it might mean that a program running on your computer is preventingWindows Update Services (SVCHOST) from accessing the Internet. Programs that might do this include firewalls, antispyware software, web accelerators, Internet security or antivirus programs, and proxy servers.

To correct the problem, you might need to add the Windows Update website addresses to the blocking program's exceptions or "allow" list or allowWindows Update Service to connect to the Internet through port 80 and port 443.

If the problem persists after you have added the Windows Update websites to your firewall's exceptions list, see thisKnowledge Base article on the Microsoft Help and Support website for additional solutions to try, or go to theWindows Update Support Center website to request support by e‑mail.