The first thing I do in situations like this is check all connections.
Turn the external drive on and off and verify you are getting power to the device -- I asume it has a power-on Light.
If everything look OK but your system still does not recognize the drive, try the following:
Shut down the computer.
If this is an external USB Box witha standard ATA drive inside, check the USB cable to make sure it is securely fastened. Turn off the power to the external box.
Restart your system. When your system comes up, turn on the external drive.
If your system still does not recognize it. Test the USB port with another device. If the other device does not work either, the problem is with the USB port. If the other device works, you know the USB port is OK so...
Try replacing the USB cable.
Open up the external enclosure and check the internal connections.
If your system still cannot recognize the drive, you may have a failed drive or faulty circuit board in the enclosure.