In case you did not know Google has a daily limit for sending email trough their SMTP servers. This is imposed in order to protect health of their server infrastructure and also affects Google Appsusers.. The limits are not small but it can happen that you will reach them and you will be locked out and unable to send emails. However you will be still bale to receive emails. Administrator can logon to management dashboard and check the User list in the Google Apps Control Panel to find details on which limits you hit and when access will be restored.
More info on the limits you can find out on Google Support pages.