If you drag files to the drive using the right mouse button, do you get any extra copy options in the menu that appears? (Try holding shift when you drag as well.)
If not, you could try using this button which makes Opus copy files via the Windows shell.
But it sounds to me like the drive is faulty if it cannot accept a long file copy, even from Windows Explorer itself, without you having to use custom "turbo" software provided by the drive. Harddrives should "just work".
It's possible there are other factors, like anti-virus getting in the way, but I'd expect that to cause the same problem with both drives, not just the Buffalo one, so that seems unlikely.