Recently after a reboot of a server, it came up as errored in our monitoring. I couldn’t ping it however when I logged into it, I could ping out ( Firewall! ). The network Profile for the Network card had changed from Domain to Private which automatically blocks ICMP and RDP.

The server might have started faster than the Domain Controller due to Windows Updates.

You can change the Profile Category of a Network Adapter per below 

Set-NetConnectionProfile -NetworkCategory DomainAuthenticated

However

Set-NetConnectionProfile : Unable to set NetworkCategory to 'DomainAuthenticated'. This NetworkCategory type will be set automatically when authenticated to a domain network.

Restarting the Network Location Awareness service fixed this and change this backt to Domain