Network Printer disappears or erratic

Environment: A small office network as 3 Windows 10 desktops, a Win10 laptops and a Win 7 laptop in a homegroup. One of the folders on a desktop ‘serves’ a shared folder and a directly attached Laserjet 5000 with the homegroup members. There’s an Epson printer attached to a network switch and it is also shared by client computers. There was a lengthy Windows 10 update this weekend.
Problem: Since the update, the HP Laserjet has disappeared from the Win 10 laptop and stopped printing multiple copies from a desktop. There’s no problem on the Win7 laptop.
Requesting troubleshooting advice.

What happens if you go into Devices and Printers and attempt to add the missing printer onto the affected machines? That's what I would try first, were I in your shoes. I noticed that after the recent FCU, I had to reset my network printers for all updated machines. This might possibly be involved. Give it a try!
HTH,
--Ed--

I wish there were a way to lock things up as you suggest/request. There is probably a way to automate the process using robokeys or something like that, but it only works as long as the UI for the configuration widgets doesn't change, either. Sigh.
--Ed--