Question : Problem: HP LaserJet 1020 stops working on Windows 2003 SBS network.

I have this same scenario in 2 totally different network setups.
The HP LJ 1020 is plugged into a workstation on the network and set to share and list in the directory (Windows Server 2003 SBS).  I have unchecked the box for Bi-Directional Support.
The printer will work for some time, allowing users from all workstations to print to it.  Then, at one point, about once a week, it will stop working.  You try to print, the job shows in the print queue for a few seconds and disappears.  The job won't print.
This happens when any workstation tries to print, even the one with the direct connection.
To resolve the issue, the printer driver must be removed, the system restarted and the printer re-installed and shared.
I have tried to update the driver, but this doesn't work either, please help.

Answer : Problem: HP LaserJet 1020 stops working on Windows 2003 SBS network.

I was thinking more along the lines of the driver getting corrupted because of communication problems between the printer and workstation caused by trying to handle a load it's not designed for.  IOW, I'm thinking that the drivers are light-duty as well as the hardware. The one with only 2 users, though, seems to argue against that, unless it's so light-duty that any amount of sharing is causing it to fail.  It might just be a bad driver to start with, but if HP doesn't have a newer one you're probably stuck.  You could try using an older style driver, like one for an HP Laserjet 5, but of course that might eliminate some functionality from the printer - I'm not sure.