have you tried stopping the windows update service, deleting everything in windows\softwaredistribution then starting windows update service and trying that update again?

Actually I did do that after posting the question.  I stopped the service, deleted everything from the download folder, and then restarted Windows and started Windows Update.

There are two more recent update files that have also been failing, KB4516065 and KB4531786.  

Update is currently trying to download those three files with 0 kb downloaded, and 0% complete.  Just spinning its wheels at the moment; don't know why.

All three of the updates failed.  This is for the subject update:

Security Update for Windows 7 for x64-based Systems (KB3126587)

Installation date: ‎1/‎2/‎2020 7:48 PM

Installation status: Failed

Error details: Code 80246007

Update type: Important

A security issue has been identified in a Microsoft software product that could affect your system. You can help protect your system by installing this update from Microsoft. For a complete listing of the issues that are included in this update, see the associated Microsoft Knowledge Base article. After you install this update, you may have to restart your system.

More information:
http://support.microsoft.com/kb/3126587

Help and Support:
http://support.microsoft.com

have you installed the march servicing stack and SHA-2 updates (required for 4516065)?

Hi Seth -- No, I don't know what those are.  Would that fix the 3126587 failures? -- Tom

try also first removing the 2-3 last updates, then start again

Hi Nobus -- the 587 update failure started in April 2018 and I was not aware of it until now.  It fails every night.  There were two "Security Intelligence updates" that were successful during the last week. -- Tom

Thanks, I started the SFC.

takes about 20 minutes

It's been sitting at 56% complete for awhile now.  Should I restart it?  I don't know whether it is still running. The hard drive light is on almost constant so I think it is running or stuck in a loop.

It's still running, just jumped to 65%.

And done.  Found corrupt files but could not fix all, so going to rerun it.

After second run, still some unfixed corrupt files.  Running again, #3.

Ran a 4th time, still some corrupted files that were not corrected.

Per WindowsSevenForums, I downloaded and am running the System Update Readiness tool.  It started a Windows Update Standalone Installer that appears to be spinning its wheels and not going anywhere.  Should I skip that and move to the Repair/Install?

FYI, attached is the SR log from CBS.
sfcdetails.txt

from your log, all errors point to  :
 CSI    00000205 [SR] Cannot verify component files for Microsoft-Windows-VirtualPC-VMSAL.Resources, Version = 7.1.7601.17514, pA = PROCESSOR_ARCHITECTURE_AMD64 (9), Culture = [l:10{5}]"hu-HU", VersionScope = 1 nonSxS, PublicKeyToken = {l:8 b:31bf3856ad364e35}, Type neutral, TypeName neutral, PublicKey neutral, manifest is damaged (TRUE)

so it's good to run the tool; but if it hangs, try a repair

Ran the System Update Readiness tool.  Ran SFC.  CBS shows the following errors (text file also attached):

2020-01-04 07:15:24, Info                  CSI    00000207 [SR] Cannot verify component files for Microsoft-Windows-VirtualPC-VMSAL.Resources, Version = 7.1.7601.17514, pA = PROCESSOR_ARCHITECTURE_AMD64 (9), Culture = [l:10{5}]"tr-TR", VersionScope = 1 nonSxS, PublicKeyToken = {l:8 b:31bf3856ad364e35}, Type neutral, TypeName neutral, PublicKey neutral, manifest is damaged (TRUE)

2020-01-04 07:15:47, Info                  CSI    00000239 [SR] Cannot repair member file [l:48{24}]"Microsoft.Common.targets" of NetFx-MSBuild_Targetfiles, Version = 6.1.7600.16385, pA = PROCESSOR_ARCHITECTURE_AMD64 (9), Culture neutral, VersionScope neutral, PublicKeyToken = {l:8 b:b03f5f7f11d50a3a}, Type neutral, TypeName neutral, PublicKey neutral in the store, hash mismatch

2020-01-04 07:15:48, Info                  CSI    0000023b [SR] Cannot repair member file [l:48{24}]"Microsoft.Common.targets" of NetFx-MSBuild_Targetfiles, Version = 6.1.7600.16385, pA = PROCESSOR_ARCHITECTURE_AMD64 (9), Culture neutral, VersionScope neutral, PublicKeyToken = {l:8 b:b03f5f7f11d50a3a}, Type neutral, TypeName neutral, PublicKey neutral in the store, hash mismatch

2020-01-04 07:15:48, Info                  CSI    0000023c [SR] This component was referenced by [l:202{101}]"Microsoft-Windows-Foundation-Package~31bf3856ad364e35~amd64~~6.1.7601.17514.WindowsFoundationDelivery"

2020-01-04 07:15:48, Info                  CSI    0000023f [SR] Could not reproject corrupted file [ml:520{260},l:102{51}]"\??\C:\Windows\Microsoft.NET\Framework64\v2.0.50727"\[l:48{24}]"Microsoft.Common.targets"; source file in store is also corrupted

2020-01-04 07:18:16, Info                  CSI    000003b5 [SR] Cannot verify component files for Microsoft-Windows-VirtualPC-VMSAL.Resources, Version = 7.1.7601.17514, pA = PROCESSOR_ARCHITECTURE_AMD64 (9), Culture = [l:10{5}]"tr-TR", VersionScope = 1 nonSxS, PublicKeyToken = {l:8 b:31bf3856ad364e35}, Type neutral, TypeName neutral, PublicKey neutral, manifest is damaged (TRUE)

2020-01-04 07:18:16, Info                  CSI    000003b7 [SR] Cannot repair member file [l:48{24}]"Microsoft.Common.targets" of NetFx-MSBuild_Targetfiles, Version = 6.1.7600.16385, pA = PROCESSOR_ARCHITECTURE_AMD64 (9), Culture neutral, VersionScope neutral, PublicKeyToken = {l:8 b:b03f5f7f11d50a3a}, Type neutral, TypeName neutral, PublicKey neutral in the store, hash mismatch

2020-01-04 07:18:16, Info                  CSI    000003b9 [SR] Cannot repair member file [l:48{24}]"Microsoft.Common.targets" of NetFx-MSBuild_Targetfiles, Version = 6.1.7600.16385, pA = PROCESSOR_ARCHITECTURE_AMD64 (9), Culture neutral, VersionScope neutral, PublicKeyToken = {l:8 b:b03f5f7f11d50a3a}, Type neutral, TypeName neutral, PublicKey neutral in the store, hash mismatch

2020-01-04 07:18:16, Info                  CSI    000003ba [SR] This component was referenced by [l:202{101}]"Microsoft-Windows-Foundation-Package~31bf3856ad364e35~amd64~~6.1.7601.17514.WindowsFoundationDelivery"

2020-01-04 07:18:16, Info                  CSI    000003bd [SR] Could not reproject corrupted file [ml:520{260},l:102{51}]"\??\C:\Windows\Microsoft.NET\Framework64\v2.0.50727"\[l:48{24}]"Microsoft.Common.targets"; source file in store is also corrupted
sfcdetails-errors-after-hotfix.txt

so it says the same as i did…
maybe test the cpu ?
online :  https://cpux.net/cpu-stress-test-online
or :  https://silver.urih.com/
downloadable :  powermax :  https://www.ct.nl/reviews/powermax-stresstest-voor-je-pc/

Maybe.  I did a repair/install and am now running Windows update needing over 100 updates.  Will see what I end up with.  If errors remain, I will check CPU.

if the repair went well - and so do the updates, i assume it is a software fault - not hardware
but it never hurts to check the temps, and with a short test test it

Hi Nobus --

Still working the updates (why do they take so long?)  Anyways, KB3126587 was successfully installed, but KB4516065 and KB4531786 still failing.  Also have a new one for Internet Explorer 10 for Windows 7 x64.

A few months ago I was getting shutdowns due to high temps.  I found a bunch of dust in the heat sink over the cpu and cleaned it out.  Temps have since been fine since.  

-- Tom

Still some Windows updates fails, as noted above, but the long term KB3126587 has been installed successfully.  

Also, I ran SFC again and it came back clean (no errors).

So, since the issue for which I posted this question has been fixed, and since the SFC came back clean, I will close this unless you, Nobus, have some further comment/suggestion.

>>  Temps have since been fine since.  <<  are you monitoring them ?

anyhow - if it is fixed after running sfc  - then that seems to be the cure

Yes, I have a temperature monitor that displays the temps.  Got it during shutdowns and led me to the problem with dust.

Okay, will shut this down.  But I may be back with the update issues that seem to be ongoing.    Thanks.

Seth -- Thanks for your quick response.

Nobus -- Thanks again.  But I still need to figure out these Windows Update failures!

tjvetter - no need to close it before you have a solution...