"Did not receive greeting from server"

[guedressel]

Hello everyone!

We just took our brand new Zimbra 7 live.
We migrated all accounts, mailboxes and other date from a Zimbra 5 server.

So far the new machine is up and running. Never the less we experience some "hickups".
Notably one error occurs for all users using the zimbra webmail client: when a mail gets sent through the webmail client most times an error dialog pops up with some java exception.
After a second (sometimes third) attempt to send the mail, it gets sent properly.

This exception is (read from mailbox.log, cut up to for beeing read better):

...
com.zimbra.common.service.ServiceException: system failure: Unable to send message
...
at com.zimbra.cs.mailbox.MailSender.sendMimeMessage(MailSender.java:630)
...
Caused by: com.zimbra.cs.mailbox.MailSender$SafeMessagingException: Did not receive greeting from server; chained exception is:
com.zimbra.cs.mailclient.MailException: Did not receive greeting from server
at com.zimbra.cs.mailclient.smtp.SmtpTransport.protocolConnect(SmtpTransport.java:182)
at javax.mail.Service.connect(Service.java:291)
...

How/where could I start further investigations?
What component do you suspect to have some issue?

Thanks,
Günter

PS: We are running at "Release 7.1.1_GA_3196.UBUNTU10_64 UBUNTU10_64 FOSS edition."

[guedressel]

Just upgraded server to Zimbra 7.1.3; problem still exists.