Please try testing for a plugin conflict. You can do this by deactivating all third party plugins, and seeing if the problem remains. If it’s fixed, you’ll know a plugin caused the problem, and you can narrow down which one by reactivating them one at a time.
If the issue persists, please get the PHP memory limit of your site increased.
To do this, please edit your wp-config.php file and insert these lines:
It appears to be security related and access to nav-menus.php is forbidden upon post. You can verify this by going to Admin > Settings > Permalink and switch it to Simple. Then go back to Admin > Appearance > Menus and re-save it, and you’ll get this
The 404 error is displayed by Wordpress once the URL is not available, this time, it’s the 403 Forbidden. That’s why switching to standard permalink disable the Wordpress’ 404 page and it reveals the actual error.
Unfortunately, this issue is something that can only be fixed by your hosting provider. I recommend contacting your hosting provider and provide them the complete procedure on how to reproduce it including the change of permalink to Simple.