Hello, I'm just a home user of Cisco Anyconenct. The software is provided via my institution's website. The name of the most current installer is anyconnect-macos-4.4.03034 -core-vpn-webdeploy-k9.pkg. (in case it is important to know)
After really a year of dealing with my computers, seemingly randomly, becoming unable to see any printers on the LAN, I realized that the problem occurs after I log into the VPN network and as soon as I log out, the printers miraculously reappear, with their queues intact, and start printing.
This happens on computers as varied as an old MacBook Air 11 inch, and the newest iMac 27 inch. I'm using the latest OS, 10.14.5, but I remember that the problem occurred with 10.13 as well.
I use the VPN to access literature only. It is not a critical part of my home computing environment. I am making this posting more as a report to whom it may concern (and to who may be interested) than a request for help. This should not happen and I should not have to do this or that to my system to have normally functioning printing while Anyconnect is active so I will live with simply disconnecting if I need to print.
I have no idea if it is a known issue on the Mac. I did some search and saw problems why LAN printing going back many years on Windows PCs.