EG has two connections: one to a workspace server (processing your job) and one to a metadata server (sort of a directory service for how to find servers, data, etc).
The metadata server connects via port 8561, and the workspace server uses 8591 (by default, these can be changed by an admin).
While your job is running, there is little-to-no traffic to the metadata server. In EG 4.1, this can time-out depending on your firewall settings and cause problems. EG 4.1 doesn't recover very well when the metadata server connection is severed. This is much better in EG 4.2.
If EG is waiting for the workspace server to finish a job, even a long-running job, EG polls the workspace server every 5 seconds or so to gather any relevant SAS logs. This should be enough activity to keep the port open even if it's got a 15- or 30-minute timeout setting.
I recommend that you work with SAS tech support on this, and be prepared to provide details about your VPN and firewall settings.
Chris