The Disappearing ActA VM went off the network, and actually lost the NIC from within the VM's hardware.
Pouring through logs, (some thanks to LogInsight, more on that later), I discovered in vmware-xx.log:
2013-11-19T07:33:01.246Z| vcpu-0| Powering off Ethernet0ah ha! This shows Ethernet0 was removed via the "Safely Remove Hardware" icon in the Windows system tray.
2013-11-19T07:33:01.246Z| vcpu-0| Hot removal done.
The solution is to add a new NIC of the same type.
This is something that happens quite a bit as you can read here: http://blogs.vmware.com/kb/2010/06/nic-is-missing-in-my-virtual-machine.html
A good idea to prevent this would be to disable HotPlug as mentioned in this KB artile: http://kb.vmware.com/kb/1012225
LogInsight was able to show some hints, but didn't quite nail it. LogInsight showed:
2013-11-19T07:33:01.841Z esxhost.local Vpxa: [FFE6FB90 verbose 'Default' opID=WFU-e9559ea6] [VpxaHalVmHostagent] 2746: Config changed 'config.extraConfig["ethernet0.pciSlotNumber"].value'
Unfortunately, LogInsight doesn't index the virtual machine logs (vmware.log). If it did, it would have saved me a lot of time.
William Lam has done a great post on how to get your vmware.log into the ESXi syslog, http://www.virtuallyghetto.com/2013/07/a-hidden-vsphere-51-gem-forwarding.html