When the host drops out of vCenter, can you SSH onto the disconnected host and check your free inodes - or at least monitor this to see if they are slowly being exhausted.
I had a similar issue in the past where the hardware monitoring service sfcbd watchdog was causing this.
Here is a KB article and the thread I posted with instructions to check this (SSH and PowerCLI);
VMware KB: ESXi host is disconnected from vCenter Server due to sfcbd exhausting inodes
https://communities.vmware.com/message/2178047#2178047
In my case it was on version 5.0 and VMWare provided a hot patch to address this.
It was eventually fixed in a general release patch, but I still run a scheduled PowerShell script to monitor this which sends out an email alert if certain thresholds are met.