Do you have any antivirus, security, or firewall applications that could be blocking Local?
More details about troubleshooting this here: Router Mode
And here:
Could you share your full Local Log here as well? For us to be able to troubleshoot thoroughly, please click the Download Local Logs button from the Support tab in Local. This will generate a zip archive that contains the Local log along with some other diagnostic information to help quickly zero in on any issues that Local is encountering.