Windows Update is so unbelievably fragile. I keep getting "Error 80072F78" on 32-bit Windows 7 no matter how many times the Update Troubleshooter "fixes" it.
I have access to Windows 10, so that's not a problem. The error is happening in a Windows 7 virtual machine, which I'm maintaining so I can have access to all previous versions of Windows (for software testing), so upgrading really isn't an option.