I've used a lot of these drives over the years and have had this happen many times. I learned data you don't backup twice is data you don't want, that's why I have a several external drives. Most times I can get the drive working but when I do I copy the data to another drive, then repartition and reformat it.
Some people never restart their mac's, I don't know why they do this but if your one of them do that and see if it works.
If not unplug the USB cable from the drive reattach and see if that works.
If not try different USB ports, after an install of El Capitan beta one of my drives stopped working on one USB port.
You can try to restart with the drive plugged in and see if it pops up on your desktop.
If this doesn't work connect the drive to another computer if you have one available, if it shows up immediately copy that data to another backup drive, if it doesn't show up the drive probably has a corrupted file system.
Try Disk Utility, this will take a long time, after it runs see if the drive works, restart your mac and look for a folder named Recovered Files in the Trash, that's where Disk Utility puts them.
If you still can't the drive to work you might want to consider third party software like Disk Warrior or a recovery service to get your data.
I wish you luck!
