are you using Addons like "Adblock plus"?

Try the reset described here:
http://kb.mozillazine.org/Problems_printing_web_pages#Reset_printer

Make sure that you reset all the print.printer preferences for that particular printer.

No there are no addon's like adblock

The popup initially shows up and the print screen flashes for half a second then disappears.

If you press Ctrl+p after that, does the print dialog show persistently or is it cleared again?

Ctrl+P brings up the print dialog but it only prints the static window. The pop up that I need to print out does not. I should point out that for security reasons the text of what is to be printed never appears on the screen. I see a blank page that is loading then the print dialog window comes up and should stay up while the blank page closes.

Did this problem just start with Firefox 21?

I wonder whether there was an intentional change to cancel the print dialog if a script in the window closes the window. I briefly looked for such a thing, but didn't find it. This kind of change can be hard to research...

I'm not sure how your device is set up, but is it an option to try a new profile? This would show how Firefox runs "uncustomized" (well, with your current plugins). In addition to bypassing current extensions and custom settings, it should have completely fresh settings databases and a fresh cache folder.

Close Firefox and start up in the Profile Manager as described in Profile Manager - Create, remove or switch Firefox profiles. Any time you want to switch profiles, close Firefox and return to this dialog. I recommend using the default location suggested, and not deleting anything without making backups first.

Does the window/dialog work as expected in the new profile?