So it has downloaded and installed the core plugin but the actual update fails?

This usually – when it happens from time to time – comes down to another plugin or WP theme trying to hijack the AJAX call. Big, security WP plugins have a habit of doing this. And it means the return codes we get from the process are wrong as they have been changed or added to. Also happens if you have turned on extra authentication processes to access the server.

So first question has to be have you changed or added anything since the last SP update a couple of months back?

Andy, in the last few month I updated some plugins and the template, just normal things.

I give you more info. 

In the plugin list, the version I have is the 5.5.9. When trying to update the database, it says it’s updating from the 5.5.8 (from 13000 to 13315). Strange, isn’t it?

After I clicked to update the dB, I right-click and choose “Inspect element”.

It shows an error “Uncaught ReferenceError: spjPerformUpgrade is not defined admin.php:460”

updating from the 5.5.8 (from 13000 to 13315).
That’s exactly correct.
If you can open your script console you will probably see other errors. Something seems to be killing your javascript session so that it no longer runs. Need to track the source of the error.

I just don’t know how to do that…

What browser do you use?

Done! You gave me a HUGE hint!

I am using a WP theme with a child, heavily customised.

I switched off the child and activated the main theme. SP uprade went through perfectly, nice and smooth. 

Put the child back and done!

Thank you for your help Andy, greatly appreciated 

I wish there was an easy way to keep themes from hijacking ajax requests, but doesnt really seem to be viable options there…  glad its resolved!