Because you mentioned the report listener, I'm going to assume you have the classic (not web) client.
Did scheduled reports ever work? Is your LAN architecture DHCP (almost all are these days). The SCCS needs to be able to "see" the client server or else it will not run a scheduled report. The SCCS must be able to resolve the computer name to do this. Check that your IT dept. has properly populated the server name of the SCCS in the DNS.
If you have Web Client (and scheduled the reports from Web Client), then follow captaingadget's advise and assign printers on the Web client server to which you want the reports to print.