We just discovered one of our older host servers was in a non-responsive state in vCenter.  After successfully confirming network connectivity of the host server and virtual machines, we determined that the problem must be the host management service was hung.

The issue was resolved by running the following command after logging into the service console:

# service mgmt-vmware restart

About a minute after successfully restarting the host agent service, the host regained connected state and full mangement of the host resumed.

Great VMware KB articles to reference:

Diagnosing an ESX/ESXi host that is disconnected or not responding in vCenter Server:  http://kb.vmware.com/selfservice/microsites/search.do?language=en_US&cmd=displayKC&externalId=1003409

Restarting the Management agents on an ESX or ESXi Server:  http://kb.vmware.com/selfservice/microsites/search.do?cmd=displayKC&externalId=1003490

Additional note:

Ray Heffer noted in his blog that if the restart hangs, then the process causing the issue must be killed.  We did not need to take this step, but if this situation occurs, Ray has some great notes for killing the conflicting process.