Can't select files in one Finder window to copy to another Finder window

I don't know why I suddenly seem to be having this problem (because I don't remember it happening before):

- I selected a group of files in one Finder window, to copy them to another Finder window (first window displayed files on removable media, second window displayed hard drive) . . . keystrokes: Click (on filename at top of the group), Shift-Click (on filename at the bottom of the group)

- I deselected two files I didn't need to copy . . . keystrokes: Cmd-Click (on each filename)

When I then tried to drag the files that remained selected, the selection highlighting kept clicking off. I couldn't find a way to get it to stay.

What am I doing wrong?

Thanks.