Hello,
SecureLine for Mac and for iOS are based on IPSec (contrary to Windows and Android versions that use OpenVPN). The Mac version uses the system-native Racoon daemon under the hood. From the screenshot it is visible that the Racoon tried to connect to the service but it failed.
To elaborate more, could you please generate a support package (Application menu->Help->Avast Technical Support->Generate support package) and create a support request (also from the menu)? This will be processed with a support knowing a Mac technical background. The support package contains sensitive data like a license ID and therefore should not be attached to this discussion.
Generally, the IPSec is more sensitive to packet loss (you can try to ping i.e. our Prague gateway 77.234.40.82 from the Terminal) and also uses different ports (50, 51, 500, 4500) than OpenVPN that are blocked for example with certain Cisco routers as a default setting.
Best Regards,
Martin
P.S. This is the first post because the Mac SecureLine forum was separated from the Mac AV forum in a today's program update