"If the Configure HTTPS binding option is unchecked and the HTTPS port is not specified, the WebSocket server does not start on the Site Server and the persistent connection will not be available."
The Altiris administrator didn't have the box checked for "Configure HTTPS on Site Servers" as shown here:
Resolution
Go to the "Global Site Server Settings" page (SMP Console>Settings>All Settings>Notification Server>Site Server Settings) and check the box for "Configure HTTPS on Site Servers" under the "Web Configuration" section.
Then update configuration on the Site Server and send Basic Inventory.
Go back to the desired Site Server Communication Profile (under SMP Console>Settings>Agents/Plug-ins>Symantec Management Agent>Symantec Management Agent Communication profiles>Site Server Communication profiles) and the option for editing the persistent connection should be available.