My previous fix for the HP LaserJet 1020 Spooler Service Restart issue did not stick. Upon reboot of the server, the problem returned and was not correctable in the manner previously described.

I researched the issue again and found a Microsoft forum post where they actually fixed the issue. The fix goes as follows:

• NOTE: Do this on the machine connected to the printer.
• Run gpdedit.msc
• Go to “Local Computer Policies\Administrative Templates\Printers”
  • Set the setting “Allow print spooler to accept client connections” to “Enabled”
• Go to “User Configuration\Administrative Templates\Control Panel\Printers\”
  • Set the setting “Point and Print Restrictions” to “Disabled”
• Close the Group Policy Editor
• Go into the Printers and Faxes control panel, right click on the printer and hit properties.
• Click the “Ports” tab
• Uncheck “Enable Bidirectional Printing”
• Close the Printer panels/windows
• Run a command line, type in “gpupdate /force”, and hit enter

Fixed!

The forum fix was here.