Is their a NAT or Proxy between your users and your mail server? If that's the case, Then the connection will not be maintained.
Try connecting a workstation to the same subnet as the server and retest, If that's a fix, You need to switch to a more robust firewall solution that will maintain the connection.
In the past, I have gotten away with a Cisco 2620 IOS/NAT as it will maintain the connection indefinitely.
Hope this Helps.
Timothy Cox
MCSE