Can't install updates since November

Just discovered that almost all my Win 7 automatic updates have failed since November. I get an 800706f7 (unknown error) message.

The last successful one was Windows Defender 915597 on November 11. The next one -- Win7 x64 update KB3008627 -- failed, as did most other automatic updates. I did notice that a few subsequent updates did go through for Malicious Software Removal tool, security update for .NET, and security update for Office 2007.

I tried restoring my machine, but it would only go back as far as November 18. No help there.

What can I do?