After a few hours of trying to find a solution to the “Installation failed” error message, when using the automatic upgrade feature in WordPress, I finally found the/my solution.
I’v tried to perform a WordPress 2.8 to WordPress 2.8.6 upgrade with WordPress installed in the website’s root folder.
Another installation of the same version located in a subfolder and used as a sandbox before updating the production installation, automatically updated without any error.
The FTP account, used for the automatic upgrades, did in this case have the WordPress installation folder as it’s root folder.
Moving the wordpress installation to a subfolder and reconfiguring the domain settings solved the problem.