Thanks for the quick response, but problems still there.
My saslauthd.conf.in is the same as saslauthd.conf now. Any of both says:
zimbra_url:
https://qa.cirrata.net/service/soap/
zimbra_cert_file: /opt/zimbra/conf/smtpd.crt
zimbra_cert_check: off
MTA settings are: Authentication Enabled, and TLS authentication only, for Global level and Server level.
In one test of outlook, I turned the SSL on for SMTP. Then I got the user/password loop. Can't go further.
In the another test of outlook, I turned the SSL off for SMTP. Then I don't get the loop. It works (sending outbound email) on the networks of the same ISP, but does not work on the networks of different ISPs.
In the third test of outlook, I turned the SSL off for SMTP. In the zimbra, I changed the https to http for saslauth files. It works (sending outbound email) on the networks of the same ISP, but does not work on the networks of different ISPs.