If so, I'd be sure the motherboard BIOS is current and check the motherboard maker for all driver updates (Windows does not do updates like this.)
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Good point. I thought to put that in to my post but forgot. They do not require a reboot to start working again. Usually within 2 minutes they are working again. It is like is it is resetting. Yesterday, my wife was uploading a large file. The USBs disconnected so the internet connection was lost. She said there was an error message, something about an unrecognized device. They the computer shut off without warning.
My AV software is updated and running. I also did a scan last night with Malwarebytes. I dont think it is virus related.
USB design includes an overcurrent feature so we don't burn them out. And right there, " 2 external WD passport 500Gb hard drives" is more than many USB ports can power.
Try it with one drive. If that helps, then you want to install some PCI or PCIe USB card. It will have it's own power system and should help.
TL;DR. Too much load. Fix with some USB card.