So you put the Nethserver red WAN Port to the Internet Router LAN Port? If you only use one interface because you are behind a router, it would be better to use the green(LAN) interface and not to have a red interface at all. But you may try disabling firewall on Nethserver for testing(shorewall clear). Can you ping outside from your Nethserver?
So the Nethserver KVM guest is working properly and you can connect from local network.
When the VM is working then I assume that the Ubuntu KVM host does his job too.
When the problem occurs, try the following:
Restarting guest vm, router, vm host one after each other and see if one of the steps solves the problem to exclude a device.
Changing dynamic ip/ddns service problems(https://www.whatismyip.com/, compare with router settings, check ddns service)
internet problems(ping ip, ping fqdn, etc.)
Can you reach the router or another lan device from wan device via wan, if you open ports? If not, the router or provider has the problem.
You may try making the nethserver to the dmz host, to port forward everything to your nethserver, if reachable then, check port forwarding rules or maybe router problem
Check ubuntu host:
Can you reach the ubuntu host from wan side? if yes, then Ubuntu with KVM has the problem.
Disable firewall on Ubuntu host, ifup all interfaces, try again
Some discussions about loosing connectivity, hanging KVM and troubleshooting Ubuntu KVM:
Cool decision, I always try to safe the systems ending up in reinstalling after hours...