Thanks, Wil.
I don't think the USB External drive is being put to sleep, as it is accessible from the Mac, meaning I see it and can access it and the data on it. Having done that, the VM Settings still DO NOT show any USB External disks. Having said that, I did check out the link you referenced and I will try the utility, "Keep Drive Spinning", to see if that helps. I'll post any results in a few days, as sometimes it takes a couple of days before it goes missing! (Points awarded IF it stays for several days!)
The VM is NOT stored on this external drive. Yes, unplugging the drive that contains the VM would be bad!!! And yes, that's experience talking! We all have to learn from experience.
Actually, I did call VMware support and they remoted in, looked at the settings and saw no USB disks available, said, "Hmmmm!", shut down the VM, restarted it and checked the Settings again, and of course the external disk was there, connected it and said, "There, all fixed.". So I thanked them, and now I thought I would ask the "world" if anyone has any ideas.
Again, thanks for your time and advice. I do appreciate it.
John