Welcome, gdcurler!
What Windows versions do you run on your laptop and your desktop? If you are using third-party backup software
(not the Windows backup), I'd suggest you try resolving the issue on your PC by reinstalling the utility.
If this is not the case, then I'd suggest you
uninstall & reinstall the external HDD as a device from Device Manager. While there, you should also check your motherboard/PC manufacturer's website for any USB hub controller driver updates and make sure you have the latest ones installed from there.
Hope it helps. Keep me posted!

SuperSoph_WD