Have you tried a different USB port on your computer? Perhaps its your USB port that is the problem. Also, you should try to plug your external hard drive into another computer and see what happens. This will help you determine if you have a problem with your computer or your external hard drive.
I don't know what you keep in your external hard drive, but have you considered backing up all of your important data in cloud storage? It's pretty convenient and there are plenty of cloud storage providers to choose from. You can be sure to find a provider to fit your needs on Top10CloudStorage.com.