Sounds a bit like power problems on the plugin drive. If the power supply isn't "stiff" enough, they will hiccup. Try it with a USB port to itself, or as the only thing on your powered hub.
My external one will only work on an onboard port, if that's any use.
Moving the files - copy them a few at a tme and ensure they are on the new drive, then delete them.
Takes longer, but when you find one that won't move, ignore than and go on down the list. That might reveal something.