Just sharing in case anyone found similar problem.

Installing Zimbra 7.1.1 and 7.1.2 (clean install) on CentOS 5.6 64 bit using
binary installer for RHEL 5 64 bit.

After installation, all services running OK except mysql.server :

[zimbra@mail ~]$ zmcontrol status
Host mail.mydomain.tld
antispam Running
antivirus Running
ldap Running
logger Running
mailbox Stopped
mysql.server is not running.
mta Running
snmp Running
spell Running
stats Stopped
zmconfigd Running
[zimbra@mail ~]$ zmcontrol -v
Release 7.1.2_GA_3268.RHEL5_64_20110804132448 CentOS5_64 FOSS edition.

Below are portion of installation logs :
...
* Starting mysql server
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
* Failed to connect to mysql...retrying
...

I could access mysql without password and found that it doesn' create any
zimbra user and databases.

Code:
[zimbra@mail ~]$ zmlocalconfig -s | grep mysql_root_password
antispam_mysql_root_password = 
mysql_root_password = zimbra
[zimbra@mail ~]$ mysql -u root -p

Enter password: 
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 119
Server version: 5.1.55-log Source distribution

Copyright (c) 2000, 2010, Oracle and/or its affiliates. All rights reserved.
This software comes with ABSOLUTELY NO WARRANTY. This is free software,
and you are welcome to modify and redistribute it under the GPL v2 license

Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.

mysql> select host,user from mysql.user;
+--------------------+------+
| host               | user |
+--------------------+------+
| 127.0.0.1          | root |
| localhost          |      |
| localhost          | root |
| mail.mydomain.tld |      |
| mail.mydomain.tld | root |
+--------------------+------+
5 rows in set (0.03 sec)

mysql>
Caused by: java.sql.SQLException: Access denied for user 'zimbra'@'localhost' (using password: YES)
at com.mysql.jdbc.SQLError.createSQLException(SQLErro r.java:1075)
at com.mysql.jdbc.MysqlIO.checkErrorPacket(MysqlIO.ja va:3566)
at com.mysql.jdbc.MysqlIO.checkErrorPacket(MysqlIO.ja va:3498)
at com.mysql.jdbc.MysqlIO.checkErrorPacket(MysqlIO.ja va:919)
at com.mysql.jdbc.MysqlIO.secureAuth411(MysqlIO.java: 4004)
at com.mysql.jdbc.MysqlIO.doHandshake(MysqlIO.java:12 84)
at com.mysql.jdbc.ConnectionImpl.connectWithRetries(C onnectionImpl.java:2172)
... 56 more
It seems that the installation setup not executed /opt/zimbra/libexec/zmmyinit, because zimbra user and zimbra database doesn't exist on mysql server. The problem only hit CentOS 5.6 because I don't have any problem on CentOS 5.5.

Solution is quite simple, just running
Code:
/opt/zimbra/libexec/zmmyinit
with Zimbra user permission after finishing installation and then restart Zimbra services.