My external drive disconnects during backup

Hi, just bought a WD Elements 1078 external 2,5’’ drive 1TB.
I connects, but when I make backup of large folder-collection, it starts copying, the white LED blinks, but after a while all of a sudden it kind of disconnects during the copy-process. The white LED is on steadily and my backup-programm tells me, that the drive is no more available.
It works on a USB2-Slot at a win7-system at a desktop-PC.
I also tried with a cable with an extra power supply plug, that means I plug the cable into two usb2-jacks at my desktop-PC. Seems the drive works longer, but after a while it again disconnects.
What might be the reason? How to prevent this behaviour?
thanks in advance

Hello,

So the unit is working on one PC or not? If yes, make sure to update the usb drivers on the other PC.

If you are not running the backup, does the unit stays connected?

The drive first is recognized correctly. After a while, during backing up lots of folders, it suddenly disconnects as described.
Didn’t try at another PC. The drivers are up to date, I checked this.
It seems, the unit stays connected until it is strained by a continuous copy-procedure.