I found the error message in the fine manual:

39           MESSAGE      REMOTE NOT ACCEPTING SERVICE REQUESTS.

             CAUSE        The remote machine has no VT servers available.

             ACTION       Enable/increase the number of VT servers on the
                          remote machine.

My question becomes:  Which is the remote machine?  From the 3000's point of
view (since it is displaying the error) somebody's PC would be remote n'est
pas?  Is our 3000 trying to connect to some other 3000?

To respond to the replies I got:

We don't have any jet direct cards on our LAN (sigh).
We don't have any ghost sessions, at least none I can see.
We get a different error (42) when sessions disconnect.

Still waiting to see if/when it happens again,
Bob