The issue is that when you try to automatically update your WordPress installation you are asked to supply your ftp login credentials. Hopefully just like me you are using unique, complex and hard to remember details. Joost De Valk created a plugin to fix the automatic update issue that some webhosts have here
The plugin (and this alternative) are a way to avoid having to go look up the details before plugging them in every time you wish to update.
In your wp-config.php you can define these values to hopefully end this problem once and for all:
define('FS_METHOD', 'ftpext');
define('FTP_BASE', '/path/to/wordpress/');
define('FTP_USER', 'username');
define('FTP_PASS', 'password');
define('FTP_HOST', 'host');
define('FTP_SSL', false);
The codex has a little more to say on the matter here