A possible reason for this is that Windows 2003 Server is set to automatically end user sessions after a certain period following user disconnection from the session. In other words when you connect to the Windows 2003 Server, start Aware IM and then disconnect from the server, it may end the session thereby stopping Aware IM.
It is possible to set Windows 2003 Server to not end sessions after disconnection. This setting is controlled in Terminal Services Configuration of Windows 2003 Server.
Running Aware IM as a Windows service is described in the Installation Guide, section "Running Aware IM as Windows service".