Windows 7 not installing updates

As of March 2017, I rarely ever touch a Windows 7 machine anymore, but I did today, and the machine was checking for updates over and over again.  I googled and found a solution in my case (below).  The machine I was working on had installed updates in October 2016.  In general, I'd say my process for updating Windows 7 machines is this:

Install the convenience update if the most recent updates were older than April 2016

If the convenience update is installed, then I'd recommend these commands from an elevated command prompt:

net stop wuauserv
net stop cryptSvc
net stop bits
net stop msiserver
ren C:\Windows\SoftwareDistribution SoftwareDistribution.old
ren C:\Windows\System32\catroot2 catroot2.old
net start wuauserv
net start cryptSvc
net start bits
net start msiserver

update rollups for Windows 7 or other OSes (convenience updates)

If (for some reason) Windows update isn't working, which oddly I've seen a couple times in the last week when I needed to update Windows 7 in advance of a Windows 10 update (the checking for updates progress bar just cycles and cycles for hours) . . .

You can install update via a "convenience" update.

As an example, here's a convenience update for convenience update for Windows 7 and Windows 2008:

https://support.microsoft.com/en-us/kb/3125574

Before installing the update, install the April 2015 servicing stack update from here:
https://support.microsoft.com/en-us/kb/3020369

Also - you may need to stop the "Windows Update" service so that the convenience update does not try to check for existing updates since the Windows Update service has already shown instability.