Host with vcenter shows enabled and running. All hosts are set to an internal time server which updates from ntp.org. If you mean the host with vcenter on it, yes, that resolves forward and backward. this was one of the most frustrating problems of my relatively short tenure, but the solution is simple enough it could help you too. Currently I have no plans to re-enable LDAP as an identity source. There are only three of us that manage vSphere so we switched to local authentication and have our usernames in the vsphere.local domain. The problems stopped immediately after we removed our LDAP identity source. We don't have a huge domain, 400 users and our VMware environment is 12 hosts.
5.5 would have at least gotten us by long enough to switch to Hyper-V. A disaster recovery would have been impossible. who cares if it's EOL this year, the 6.5 was practically unusable. We were ready to give up and go back to the 5.5 appliance. It's pretty much the same story as I've read on so many Google results. some days it was not even usable and others it was just good enough to get by. tried IE, Chrome, Firefox, tried HTML5 and Flash. the problems began pretty much immediately.
I performed a migration from vCenter Appliance 5.5 to vCSA 6.5.