I'm having a very similar, if not identical issue. I'm running Big Sur (11.2.3) and Cisco AnyConnect 4.9.05042. I think I only have this problem while I'm connected to the VPN. When it does happen, I've noticed that a ping to google.com will fail. To fix it, I've been running "sudo dscacheutil -flushcache; sudo killall -HUP mDNSResponder" and it will recover almost immediately. I really would like to resolve this issue, so I'm going to look at installing some of the tools and submit a bug report that were suggested above. I don't know if this is related to a samba connection, as I do occassionally connect to our fileshare at work. It's very annoying and I haven't been able to pinpoint exactly what the circumstances are that cause it.