VMWare guys had no idea about it and after 3 hours on the phone with
them with little progress I started experimenting on my own and found
the solution.
Remember that I migrated my VMWare Fusion hosted VMs to ESX using the
VMWare converter tool. Prior to conversion I removed all snapshots
created by VMWare fusion.
The symptoms were that the machines under ESX were losing time and
network connectivity intermittently with no log entries on ESX and no
errors on the machines other than the massive time jumps. You could
see the machines "disappear" for 2+ minutes at a shot.
Turns out the issue was VMWare Fusion's autoprotect feature. I didn't
disable that on the VMs prior to migration and while ESX doesnt
support that feature it appears to break it. ESX was creating some
kind of snapshots frequently and there was no way at ESX to disable
this functionality.
My solution was to use VMware converter to go back from ESX, load the
machine into VMware fusion, turn off the Autoprotect feature, then re-
convert the machine back to ESX. Since then everything has been perfect.
The VMWare support people were friendly but not helpful and despite
the obvious client hangs and lots of snapshots getting created by ESX
were unwilling to admit it was an ESX issue. Obviously if my fix above
fixed the issue then it was a VMWare issue. I made no changes to the
guest operating systems.