Is your Prograde reader the one that uses USB-C? When using USB-C to USB-A cables it's really important to make sure it's actually a USB3 cable, as USB2 cables are available (just to make matters nice and confusing). If it's a USB2 cable, it's possible that though even if it's backwards compatible with USB2, it could draw more power than USB2 allows, which could explain why it disconnects when you attempt to copy files. Without knowing the exact model of reader though, I can't really say. It is entirely possible that it's not backwards compatible with USB2 at all.
From what I can remember about the Z640, all of the front ports are USB3.0, so that shouldn't be a problem.
Using something like USB Device Tree Viewer (
https://www.uwe-sieber.de/usbtreeview_e.html) you will be able to see what speed the device is actually running at.