I have a p1606dn, and it does often get uninstalled by incoming packages, especially CUPS packages. Here is the note that I wrote to myself a couple years ago:
"#hp "filter failed" error
Alt-F2 "kdesu hp-plugin -u --required --reason 0"
give password, accept default "download from hp server" choice, etc.
or use interactive (text) mode in terminal:
~/$ dbus-launch hp-plugin -i --required --reason 0
The firmware lives at /usr/share/hplip/data/firmware"
But, I think we don't have "kdesu" any more, so just open a terminal and issue the terminal command.