Sims 4 Update Fail

So, I was having this problem too and found like 800 threads on this, all with absolutely no answers.  I was able to fix it on mine.

When I had the issue occur, I tried booting the game using The Sims 4 icon without Origin open, which I believe is what gave me this problem.  I say this because after finding no answers to this problem, I was going to give up and try uninstalling/reinstalling, and it told me that "thesims4.exe must be closed" before I could continue uninstallation, but I was never able to actually run that due to the lack of update, so it seemed pretty fishy.

I couldn't find the process in my process tree, so I just went ahead and did a full log off of my PC's Username.  Logged back on, went in to Program Files (x86) > Origin and ran Origin as Admin.  As soon as it opened, it told me there was an update for The Sims 4, which was slightly different than the first time (I had to select Play on the first times when it was giving me the 'Update Failed' message).  I started the update, and it went through with no issues.

So long story short, I think that Origin was registering The Sims 4 as being open, preventing the Update from completing successfully, as logging off and back on (I actually did a full reboot, but I think logging off and on would do the same, but simply rebooting Origin itself did not work) fixed the issue.

Let me know if this works for you.