If your Time Machine External Hard Disk is 5 years old or older then it may have simply died. Please try another cable, USB port and finally if you can see the External Hard Disk in Disk Utility then download and run the free version of DriveDX on the External Hard Disk. If the External Hard Disk shows any errors that indicates it has died.
All hard drives die, the question is when which is completely unpredictable. It is smart practice to replace EHD's about every 5 years or do, particularly backup EHD's as they have a habit of dying when you need them most!!
I strongly recommend the OWC Mercury Elite Pro line of EHDs.