Windows could not check for updates automatically (Important) -V. Slow

There's a lot of data missing from the file?
Did you get any error messages? - did you allow it to complete before posting it?

Still a lot missing - but one more piece added to the puzzle shows...
TrustedInstaller service stopped with error code 126 (which is the same as we'd seen it before in the Event logs)

I think I really do have to see at least the CBS.log file if it'll compress down to below 20MB on its own
You could upload the whole 80MB folder to a fileshare site (preferably Dropbox or OneDrive), and post a link

Close but no cigar - the file is dated about 3 weeks ago, and contained no errors at all
How big is the CBS.log file in the current CBS folder?

Oh wow - here's one I've never seen before!

Code:

2015-09-03 23:25:32, Info                  CBS    Fallback code servicing stack search path during setup...
2015-09-03 23:25:32, Info                  CBS    TI found cbscore.dll at: C:\windows\servicing\0.0.0.1
2015-09-03 23:25:32, Info                  CBS    Failed to load Core DLL from path: C:\windows\servicing\0.0.0.1\cbscore.dll [HRESULT = 0x8007007e - ERROR_MOD_NOT_FOUND]
2015-09-03 23:25:32, Info                  CBS    Failed to initialize CBS Core. [HRESULT = 0x8007007e - ERROR_MOD_NOT_FOUND]
2015-09-03 23:25:32, Info                  CBS    Ending TrustedInstaller initialization.
2015-09-03 23:25:32, Info                  CBS    Failed to initialize Trusted Installer. [HRESULT = 0x8007007e - ERROR_MOD_NOT_FOUND]

The news is not good
Before I pronounce sentence, please open an Elevated Command Prompt and run the following command...

REG QUERY "HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Component Based Servicing"

Post the results.
Here are some instructions to make life easier :)
1) To open an Elevated Command Prompt Window (the ECP window), click on Start, All Programs, Accessories – then right-click on Command Prompt, and select Run as Administrator. Accept the UAC prompt.
2) To run the commands easier, highlight the block of commands, and right-click on the highlight – select Copy. In the CP Window, click on the black/white icon at top left – select Paste. The commands will run but may not complete the last command, so hit the Enter Key once.
3) To copy the results... click on the Black/White icon in the top left, and select Edit... 'Select All', and hit the Enter key - then use Ctrl+V or r-click+Paste to paste it into your response.