Not sure what you have tried but try updating from a new user account.
Create a fresh user account having admin privileges on your computer.
Try installing the update again from the new account. If successful the product gets updated for all users on the computer and you can switch back to your regular user account.
If that makes no difference, try deleting the updater folder.
On Windows go to the start menu and type into the search box %localappdata%
Press return and that should take you to the following location:
Double click on the Adobe folder and delete the AAMUpdater folder
Then try the update again.
On Mac OSX go to:
I tried the new user account, but the update failed in the same way as with my original account.
I also deleted the AAMUpdater folder (as also suggested by F.McLion above) along with the AAMUpdater folder in C:\ProgramData\Adobe, but the update still fails every time at 49% complete according to the progress bar.
Are you using a firewall/internet security/anti-virus software? If so try temporarily disabling during the update and the enable again after installation.
Also try patching from one of these download links.
I had already tried disabling the firewall and anti-virus software without success.
However, you have hit the nail on the head! From the URL you gave above, I moved down to the section headed What if the computer that Lightroom is on is not connected to the internet?, downloaded the zip file under Lightroom 6.1.1/2015.1.1, ran it, and bingo - Lightroom 6.1.1 is now installed and running! The computer was, of course, on the internet, but that method of updating must have bypassed whatever the problem was that was preventing the standard method of updating from working.
Thank you very much for your efforts on my behalf.