After checking for :
- Permissions and all seems to be okay.
- Php config settings (memory_limit, max_execution_time etc) all are set at adequate values, so they shouldn't be a problem.
This seemed to be a problem caused by the hosting provider's malware scanner. The restore.php script
('administrator/components/com_joomlaupdate/restore.php') is missing and causing this error - also shown in the browser's console as:
Failed to load resource: the server responded with a status of 404
I know about this hosting provider malware that is deleting other essential files from Joomla core and extensions - I had faced similar issues with K2, Akeeba BackUp and other extensions in the past.
So, doing a Google Search about this issue, it seems that other users in other hosting providers face similar issues, and they can't find what's wrong.
In such case - and after checking for the other common possible causes, like file permissions and php settings, the solution to update your Joomla, is to manually restore the Joomla Update component files that are missing and then do the update from the backend if in the meanwhile their scanner won't delete again your files.
The other solution would be to try to update by installing the appropriate update package through the extensions installer.
As always, backup before performing any such actions.
Re-think about your hosting provider - as it's unacceptable that they are deleting essential files from your site, without notifying you.
Ok a small update notice:
To not blame all hosting providers out there if it happens as such issue for you, in some cases, this can be happened by a prior corrupted installation of Joomla, or even manually if someone deletes this or other essential files.