I faced the same problem as I tried to pump several mails as part of load testing, nearly 100 mails in a minute. After sending 500 mails, Gmail started rejecting the connection with the same error.
The situation became normal after I introduced a think time of 1 second, limiting the outgoing mail at < 50 per min.
For me, Gmail was rejecting my mails only for a duration of 3 minutes.
