When Plesk update itself, it connects to local MySQL server.If it can not connect, then update fails. Most of the time it happens because of wrong credentials.
First check if you can manually connect to local MySQL server:
"%plesk_dir%Databases\MySQL\bin\mysql.exe" -uadmin -p<type password here> -localhost
If you can not connect then you may reset the password by using following command:
"%plesk_bin%\dbclient.exe" --direct-sql --sql="Update databaseservers set admin_login='<MySQL user name>', admin_password='<type password here>' where host='localhost' and type='mysql'"
After resetting the password again repeat the step one to check whether you can connect to MySQL server, if you can then next time error won’t appear when you update.