How are you importing?
If you are connecting the camera to the computer, try using a card reader. (preferably one that's built into the computer)
This is not only faster, but also safer, because there is less hardware involved, and less things that can go wrong.
Thanks Per. Importing using external card reader connected to USB 3. I've been using Lightroom for around 7 years (always latest version) and this problem came during last months so I'm pretty sure it's SW related.
Make sure you don't have a malfunctioning card reader and/or malfunctioning USB port.
Try to import using different hardware and different USB port.
I have the same problem. I am importing from camera Canon 7D directly. It was always working with LR4. Now I got LR6CC and the problem started. And I am not going to use card reader, so that kind of advise is useless, sorry. It fills like I got a downgrade from LR4 to LR6cc instead of opposite.
But I specifically said you should "try to import using different hardware and different USB port" ...
Did you check the USB port? Did you check the USB cable? Did you check to make sure the card is working properly? Did you try a different card?