My experience with this was in Thunderbird, but the principle's apply to all.

The Problem

When attempting to send mail, the client gets an error "The message could not be sent because the connection to the SMTP server smtp.gmail.com timed out" or "The message could not be sent because the connection to the SMTP server smtp.gmail.com was interrupted"

Solutions

• Make sure your client is setup according to these directions
• Try smtp.gmail.com and smtp.googlemail.com for the server name
• Try port 465 or 587 for the port
• Try SSL/TLS or StartTLS for the encryption
• Google limits the number of connections per account to 10 per second.
• Login to your Google account and go to the reset page
• set your client check every 15 seconds
• Limit your number of IMAP connections to 2
• Check your content filter. Our filter, iBoss, was set to block webmail access unless you were logged in. Our provider's implementation of iBoss tied into their DNS servers, which gave us bad DNS entries for Thunderbird to use. This resulted in intermittent issues with Thunderbird. If the staff member was logged into iBoss, everything was fine. White listing gmail.com and googlemail.com resolved our issue.