Generally speaking, external hard drives have a shorter lifespan than internal ones, and that's particularly the case with Seagate ones in my experience. See if you can test it with SeaTools: http://www.seagate.com/gb/en/support/downloads/item/seatools-win-master/
If SeaTools can't detect it either, open Disk Management in Windows Control Panel to see if it just needs a drive-letter assigning to it.
If it isn't shown in Disk Management, assume the worst and replace the drive.