Do you have a Web Director too or just a hardware load balancer?
If someone connects to a secondary server directly and continue to stick to the same, there's really no reason why an error like that should popup
1) unless there was a real crash of an SDM program OR
2) the connection was still intercepted by a firewall (consider secondaries in DMZ) of some sort and closed the connection after a few seconds of idle time.
There maybe other scenarios though, where in a web page or something was coded in such a way that some entry still looks for your load balanced SDM alias as opposed to just the local server based entries. That could result in your request being sent to the load balancer behind the scenes again.
If you were to open a browser on the secondary server itself and point to the local SDM web server, are you seeing a similar error?
_R