We've a vcenter appliance (6.0) and each morning when we come in we are unable to login we have to restart the VM. All logins are failing (inc vsphere.local).
Top on the appliance doesn't show anything wrong (the console & ssh works fine). web client & web client both fail. The error is just the vcenter times out or fails to respond.
Hard to say without any details. Anyway I'm pretty sure the reason for this can be found in the log files.
If you have an active support contract, I'd suggest you open a support case with VMware.