If your network is down, then I am wondering how your Server is still under production. It might be that the virtual machines portgroups are managed by a different vswitch with another uplink.
However, coming to your topic, the "greyed out" options might arise if you have enabled DHCP and the removal of the vmnic0 lead to reclaiming of the IP based on the new mac address from vmnic1 which for many reasons could fail. [dhclient timing out on vmnic1, no ips, still queries with vmnic0 mac address]
I also find that the VMkernel port is treated as a virtual machine portgroup instead of management.
Check this page, since it almost similar to your case. vSphere 5 Networking Bug #2 Affects Management Network Connectivity - VMtoday
Also, I would suggest, to unlink the vmnic1 from the vswitch0 and delete the portgroup Management_network and create a new one as suggested by skan with
esxcfg-vmknic -a - i DHCP -p VMKernel