OK.  I'll answer my own question...

After working with VMware Support and the VMware Dev Team, they have concluded that the 7.11 & 7.12 agents do not like having the C:\windows\Temp\ folder purged/cleaned up prior to taking a snapshot.  More specifically, the c:\windows\temp\vmware\ folder needs to be there, as the Agent will not recreate it if deleted.  This has been resolved in the Horizon 8 agent, when the VMware subfolder will be recreated if missing.

Our issue was that we ran a few cleanup scripts as part of prepping a Master Image, prior to shutting it down and creating a snapshot.

Who would have known that we would break things by purging C:\windows\temp\ !! 

John in Tampa