Seems to be an error from PEAR Net_Socket, probably a few more lines of the backtrace would reveal that this came from Net_SMTP?
"Not connected" likely indicates that the remote SMTP connection has dropped the connection - this could be for a number of reasons, including intentional disconnection on that server's part ("whoah, 250 messages at once?!"), or an issue on that server, or even a network issue between CiviCRM and that server.
Since you say this is GMail, I'd guess that you might be running into intentional sending restrictions on Google Mail.
To keep our systems healthy and your accounts safe, Google Apps limits the amount of mail one user can send. Limits restrict the number of messages sent per day and the number of recipients per message. After reaching one of these limits, a user can't send new messages for up to 24 hours after the limit was exceeded, but they can still access their account and receive incoming email.
I don't recommend using Google SMTP for CiviMail, they will shut you down (even mid-connection!), because the service is not intended to be used as a bulk mail provider. That's not a bug, it's part of the package.
mail() method will work, but may also be limited by the hosting environment. For example, one popular webhost limits outbound emails to 150/hr and silently drops delivery of any mails beyond this. That's a situation where you might run a few test CiviMails successfully, then push out a large promo and be left confused at why the response was so poor ...
If you want to be assured of your CiviMail delivery, make sure you have established terms with your SMTP provider & make sure they accommodate the level of usage you need.