as the printer. When you disconnect from the VPN, you leave that subnet and then can't see the printer again.

If thats the case, you should be able to connect to the VPN, log into your printer's configuration (often that is as simple as typing the printer's IP address into your browser), and change it to either get its address from the same DHCP server that your non-VPN systems get their address from, or statically give it an address and subnet mask in the same subnet as you.