>[оверквотинг удален]
>>Feb 24 12:45:53 client courierpop3login: Connection, ip=[::ffff:127.0.0.1]
>>Feb 24 12:46:05 client authdaemond: failed to connect to mysql server (server=127.0.0.1..,
>>userid=postfix..): Access denied for user 'postfix..'@'localhost' (using password: YES)
>>Feb 24 12:46:05 client courierpop3login: LOGIN FAILED, user=kate, ip=[::ffff:127.0.0.1]
>>Feb 24 12:46:05 client courierpop3login: authentication error: Input/output error
>
>тут же четко видно что у тебя лишние длве точки в логине
>
>
>Аccess denied for user 'postfix..'@'localhost'

client:/# cat /etc/courier/authmysqlrc

MYSQL_SERVER 127.0.0.1      
MYSQL_USERNAME postfix        
MYSQL_PASSWORD postfix        
MYSQL_PORT 3306            
MYSQL_OPT 0
MYSQL_DATABASE mail        
MYSQL_USER_TABLE users        
MYSQL_CRYPT_PWFIELD password    
#MYSQL_CLEAR_PWFIELD password    
MYSQL_UID_FIELD 1001        
MYSQL_GID_FIELD 1001
MYSQL_LOGIN_FIELD email        
MYSQL_HOME_FIELD "/home/vmail"
MYSQL_MAILDIR_FIELD maildir

С логином все правильно.