Is this the only USB device that you're having problems with? If so, the chipset for the drive enclosure may be bad. If you have access to another computer, try it on that.
This happened to me once. What I did was crack the backup drive open (do so carefully) remove the drive & purchase a new enclosure from Newegg, or better yet, a docking station. Many are USB3, but it's backwards compatible with USB2.
Also, make sure that the proper USB controllers/drivers are installed on your computer. Those that come from Windows Update are often old, sometimes as old as 2001/2002. Go to the OEM of the computer & find the original driver.
Cat