I assume this is an external HDD.
1- Try it on different USB ports.
2- Try it on another computer.
3- Try a different cable.
If none of the above works then this may be an issue with either your HDD or the adapter inside connecting from HDD to mini USB.
At this point you can, at your own risk and responsibility and if you are very comfortable with what you're doing, open your external HDD, put it directly inside your laptop replacing the one that is already inside and see if it runs.
This is sort of a last resort and not at all recommended if you don't know what you're doing because you need to disassemble the external HDD and your laptop if you are using a laptop.
Let me know what happens in the first 3 suggestions in order to...