Ahhh, OK, I think I get you now, thanks. So, you have an issue with the server side connections remaining idle for too long?
So, the idle timeout is controlled by the TCP profile assigned to the Virtual Server. The default value is 300s/5mins which is fine in most cases. I'd suggest you create a custom profile with a lower timeout and assign it to the VS server-side only.
Enabling the OneConnect feature should also help to reduce the number of server-side connections as it will re-use them.