We moved the laserjet 500 printer to a new vlan and now it stays in the mdns database. We also disabled all other protocols than 9100, LPD, bonjour, airprint and mdns.
We have HP Laserjet 500 color M551 which is does excatly the same thing. It will remain in controllers mdns database for 4500 seconds and then disappears. Our HP LaserJet 400 M401dn is working fine and also a Lexmark CS410dn.Br. Jukka
I discovered that only printers that advertise _universal._sub._ipp._tcp.local -service string show up in iPad's printers list. So check that you have HP Photosmart Printer 1 -service snooped.Br. Jukka