Error: We couldn’t complete the updates, Undoing changes. Don’t turn off your computer.

Ron,

Are you getting any error codes which might provide a clue as to why it's failing?

Also, have you tried checking your hard drive for errors?

Here are the steps to take.

Right click the Start button, go to Command Prompt (Admin) and run the following command to check your hard drive for errors. If you have an SSD drive, run:

CHKDSK /f

If you have a standard rotary hard drive, run this command instead:

CHKDSK /f /r

You'll get a message that the tool cannot be run because the disk can't be locked and whether you want to schedule a diags check on the next reboot. Click "Yes" and then either reboot immediately, or finish what you're doing and then restart.

If CHKDSK finds bad sectors, it will mark them as such so that they can't be used. But if the tool appears to hang for more than a few of hours at a certain percentage, then that might  indicate that your hard drive is failing and will need to be replaced.

M$ doesn't appear to be releasing it manually though. All I can find on the official download channel are these two, both dated 5 May.

@Xircal, I wonder if the updates were only made to the Surface Pro version of the update.

I spoke with Level 2 support and told him all of the steps we had tried so that he would not waste another couple of hours retrying the same things.  He finally levelled with me that "the only thing that has been working for people who have this "undoing changes" problem with KB2919355 is to wipe your system and restart the update process from your original media.  

@RonSarid, I  am also experiencing supposedly successful installs on an x64 system followed by a rollback during the reboot. The last time I tried to get an update from Microsoft was not a pleasant experience - no-one had any new information but instead of getting that information for me insisted on taking over my laptop again.  Attempts to escalate to Level 2 were refused.  

I escalated through the Canadian Microsoft office and got a callback yesterday from the Microsoft Global Escalation Team.  The support person renamed c:\users\default, recreated the folder but was unsuccessful at getting KB2919355 to install.  Today I was informed that the best bet was an in-place repair - although the apps would need to be re-installed, user data would be unaffected.  I will be able to test this recovery method within the next week or so.  

My suggestion to those who are still experiencing issues is to follow the process (painful as it might be), escalate if necessary, ensure that Microsoft collects the required documentation using the Microsoft Support Diagnostic Tool (msdt.exe, requires a passkey provided by Microsoft Support) and keep escalating through whatever channels are available until you get what you need.

@Xircal, I wonder if the updates were only made to the Surface Pro version of the update.

You might be right, but according the Surface site, there weren't any updates released in June at all: http://www.microsoft.com/surface/en-gb/support/install-update-activate/pro-update-history

I finally backed up everything, used DVD recovery media to start all over again, did all updates, then reinstalled programs and data.  Now everything works and computer is decidedly faster.  I am not an IT professional, but I can think of a few things that may have contributed to not being able to do The 8.1 KB2919355 updates.  It may be that others with these problems have done some of the same things, so if we can find a common thread,perhaps we can avoid this in the future, or Microsoft an come up with a fix:

1.  I bought my Lenovo Yoga 13 with a 256 gig ssd.  After manipulating the partitions, I lost my restore partition although the unit worked properly.  Then I bought a 512 gig and used EaseUs Todo Backup and created an image of the entire 256 gig and restored it to the 512 gig.  I also bought the DVD media from Lenovo so I could once again have a factory fresh system if I desired.  I used that media on the 256 gig hard drive and used diskpart to compare the factory partition structure ("detail part" command) to what EaseUs Todo left me on the 512 gig.  Although the 512 gig system worked, several of the partitions had changed "attribute" values and some had drive letters and were not hidden as originally they were.  Also they had offsets that were not original.  I used diskpart to reconfigure the partitions to match the factory, but the offsets were definitely different and I did not change those because I did not want to risk making the drive unbootable.  So EaseUs did a poor job of faithfully restoring the partition structure and may have caused problems that did not show up until KB2919355.
2.  I installed both my 256 and my 512 gig SSDs in my Lenovo Yoga 13.  The unit recognized and assigned drive letters to each. When the update form 8.0 to 8.1 happened, it failed time and again.  When I removed the 256 gig drive, the update worked as it should and I again put the 256 gig back in.  I wonder if having both drives in there may have compromised some update(s).  After all, 8.1 would not even install with it, so couldn't some other update have installed improperly?
3.  I used Ccleaner to clean the registry.  Is it possible that ccleaner "cleaned" something that should have been left?