– Any error message?
– Please check the error logs on your server for a more specific error message and see why it’s failing. If you need help locating them, ask your hosting provider to help you with that.
– If you cannot find error logs or if you don’t find any helpful info in the error logs, try Enabling debugging

side note to @wroose,

please do not jump into other topics. If the troubleshooting already posted made no difference for you, then, as per the Forum Welcome, please post your own topic. That way you stand a good chance of getting the assistance you want. Despite any similarity in symptoms, your issue is likely to be completely different because of possible differences in physical servers, accounts, hosts, plugins, theme, configurations, etc. Thus one problem, on one setup is not indicative of the functionality and reliability of an application as a whole.

Try:
– deactivating ALL (yes all) plugins temporarily to see if this resolves the problem (plugin functions can interfere). If this works, re-activate them individually (one-by-one) to find the problematic plugin(s).
– If you don’t have access to your Dashboard’s Plugins page, try manually resetting your plugins (no Dashboard access required). If that resolves the issue, reactivate each one individually until you find the cause. Also remember to deactivate any plugins in the mu-plugins folder (if you have created such folder). The easiest way is to rename that folder to mu-plugins-old.
– switching to the unedited default Theme (Twenty Seventeen) for a moment using the WP dashboard to rule out any theme-specific issue (theme functions can interfere like plugins).
If you don’t have access to your Dashboard’s Appearance page, access your server via FTP/ SFTP , or a
file manager in your hosting account’s control panel (consult your hosting provider’s documentation for specifics on these), navigate to /wp-content/themes/ and switch to the
default theme by renaming your current theme’s folder by adding "-old" to the end of the folder name. Alternately, you can remove other themes except the default
theme (Twenty Seventeen). That will force your site to use it.
– If the above steps do not help, try MANUALLY updating. Download WordPress again and unzip it. Access your server via SFTP or FTP, or a file manager in your hosting account’s control panel (consult your hosting provider’s documentation for specifics on these), and delete then replace your copies of everything on the server except the wp-config.php file and the /wp-content/ directory with fresh copies from the download. This will effectively replace all of your core files without damaging your content and settings. Please read the Manual Update directions first.