If the SMC reset does not help, read on:
Is the drive a "bus-powered" drive?
That means it has no separate power supply and has to get all its power from the computer's USB port. Electric motors like the one that spins the hard drive platter have a tendency to demand more power as they age; a drive that worked fine for several ytears can suddenly not mount. It can get power to turn the drive or operate its data interchange hardware, but sometimes not both.
If you have a bus-powered drive, there are a coupl of inexpensive steps that may restorre its function:
1) get a USB "Y" cable. Its "computer end" plugs into two USB ports to provide more power. Cheap and ofter wotks. Here is a link
http://eshop.macsales.com/item/OWC/USB2AYMBPB/
2) Use a Powered USB hub between the computer and the drive. A powered hub has an independent power suplly and make up for wha tthe computer cnnot provide. Link:
http://eshop.macsales.com/item/Syba/CLHUB20127/