The most likely cause of is that the users Outlook or other e-mail client is set up to authenticate to the mail server when they first login and again when they receive e-mail. This authentication allows them to send and receive their e-mails with no problems. But there is a time limit for this authentication of 30 minutes. This is in place to prevent open authentication which can be abused by spammers. Once the authentication is expired, if a user tries to send an e-mail without authenticating again the server will reject the e-mail with the "We don not relay" message.
There are two ways to avoid getting this error. One is to authenticate on outgoing messages and the other is to set the e-mail client to check for messages automatically within the 30 minute expiration period. Since Microsoft Outlook 2003 is the most common e-mail client we deal with that is the one we will describe the configuration for but most e-mail clients will have a similar configuration.
1) To authenticate outgoing messages,
Within Outlook select Tools from the menu bar
Select Email Accounts, this will open a new window
Select View or change existing e-mail accounts and click Next
Highlight the e-mail account name and click Change
Click the More Settings button
Select the Outgoing Server tab
Put a check in the box for My Outgoing Server (SMTP) requires authentication
Select Use same settings as my incoming mail server
Click OK, click Next, and click Finish
2) To automatically check for messages,
Within Outlook select Tools from the menu bar
Select Options, this will open a new window
Select the Mail Setup tab
Click the Send/Receive button
This will bring up the Send/Receive Groups window
Under Group Name be sure that All Accounts is highlighted, but do not double click it
Below this is the Setting for group All Accounts
Check the box next to Include this group in send/receive(F9)
Check the box next to Schedule an automatic send/receive every
In the box next to this enter the number of minutes between each automatic send/receive, ** see below
Click Close, click OK
** This setting should be between 2 and 30 minutes depending on the speed of your Internet connection. If the setting is too low it is possible that the download of e-mail would not complete before the e-mail client initiates its next send/receive process. This will result in incomplete downloads and messages being downloaded repeatedly. If the setting is above 30 minutes your authentication will expire. Generally 5 to 10 minutes is a safe setting.