Q: HP Laserjet 5MP keeps going offline

Hi,

I've got a HP 5MP Laserjet connected to a 27" iMac running Mavericks 10.9.5. Connection is via a parallel to USB adapter cable, and the printer keeps going offline. When it does, I can still print, but I have to hit the pause/resume button in the print queue box for every job. There doesn't seem to be any predictable action that kicks it offline. The printer ran flawlessly on a variety of other older computers running Tiger 10.4.11.

Remedies I've tried so far:

1) Resetting the printing system (right clicking in the white space below the list of printers in the Printers & Scanners dialog box)

2) Reinstalling the OSX driver (19.13). At least, I assume that I reinstalled it. I downloaded from this support page and assume it would overwrite the existing driver which is also 19.13

HP Printer Drivers v3.1 for OS X

3) Removing and reinstalling the printer (numerous times) in the Printers and Scanners dialog box

4) Resetting the printer by removing the power cord for 60 secs and restarting the printer and desktop.

5) Performing a cold reset on the printer by powering down, then restarting while holding down the rear-most (orange) button on the control panel for less than 20 seconds.

These actions typically solve the problem, but only temporarily.

Any ideas would be GREATLY appreciated.