In Disk Utility select that external drive then click the Partition tab. Then select One partition from the Partition Layout drop down and make sure it is set to a GUID partition table, that is under the Options button, and the format is set to Mac OS Extended (Journaled).
Then Click the Apply Button. If the drive is still good it will be partitions and formatted and then can be used for a TM backup drive.
But I suspect either the drive is failing or the electronics in the drive enclosure are failing. In the first case there isn't much you can do about a failing hard drive except replace it. On the second part if the enclosure electronics are failing then you can take the physical hard drive out that enclosure and connect it to your mac with a SATA to USB adapter or put it in another enclosure.
Then you have the simple fact the Apple Mac notebook computers always seem to have a problem with these USB Bus powered external hard drives. It seems the USB port on Mac notebook don't put out enough power on the USB port to fully power up these type of drives. They do some times but not always. One work around for that is to use a Y USB cable that connect to 2 USB ports at the same time to supply more power to the drive.