In some slower shared host environments (for example, godaddy.com), the automatic update methods can fail in some cases. This appears to happen when the server is busy and the update is unable to complete within a given amount of time (for example, in 2 minutes for godaddy.com).
In this case, the update may be partially completed and the site may be damaged. You can repair the site using the Manually Copy New Program Files update method.
Also, there is a free third party extension called Admin Tools that can do updates on slower shared host systems.