i searched support.microsoft.com under 'Windows Update' keyword '0x80072F05'only one article found (326253 - You Cannot View Updates on the Windows Update Site Using Secure Socket Layer) and not quite your symptoms maybe but right error number and some easy things to try.
complete article has full instructions for each 'step'...
After you scan for updates on the Windows Update Web site, you may receive the following error message:
There are no updates available at this time
There are no updates available for your computer. Please check back later.
Additionally, the menu on the left side of the page is shaded, and the Pick Updates to install link is unavailable.
You may also be prompted to file an error report that is similar to the following error report:
Software Update Incomplete
The Windows Update software did not update successfully.
Send error number to Microsoft (0x800A138F)
Finally, he Windows Update.log file may contain a message that is similar to the following message:
Error IUENGINE Querying software update catalog from https://v4.windowsupdate.microsoft.com/getmanifest.asp (Error 0x80072F05)
CAUSE
This behavior may occur if one or more of the following conditions are true:
The computer's date and time settings are incorrect.
Neither of the following Advanced Internet Explorer settings have been selected:
SSL 2.0
SSL 3.0
Internet Explorer is not accepting the redirection of Common Gateway Interface (CGI) information from a non-SSL server to an SSL server.
"English (United States) [en-us]" is not the first item in the Internet Explorer's Preferred Language preference list.