Have an HP Envy 5665 All in One Printer, bought a few months ago. Setup was easy, and it was working well for a while. Recently, we had issues printing. When printing a file, the Printers/Scanners window showed that "Printer was not Connected" even though the wireless was working fine for other devices. The Network Configuration Page showed that the Internet was "Not Connected". Deleting the printer from the Printers/Scanners window and trying to add it back in (clicking the + sign) didn't work either - the computer was not able to recognize the printer to add it back on.
Rebooting the printer (power cycling off and on) works for about 2-3 print jobs, and then after a minute it goes back to "The printer is not connected" error message. I even tried downloading HP drivers for my operating system to no avail.
We had this issue with a previous HP, too. Very frustrating to constantly have to cycle on the printer/modem just to get a couple of print jobs done.