I have exactly the same problem and already do the Time Machine backups but bought the Seagate Plus Slim in order to save all my photos and videos on an external hard drive so I can get them off my MacBook Air and have them in 2 places. Just followed the steps to erase the drive and then selected 600 photos to export but it didn't work --- a window came up explaining the export operation failed and it listed the first 100 photos with error explanation on each that the file 'couldn't be opened because there is no such file'. What could this mean?
The Backup Plus Slim offers 1TB or 2TB of storage, and the Backup Plus Portable is available with either 4TB or 5TB of storage space. Both are formatted to work with either Mac or Windows. Plug in your Backup Plus to your system. Open Time Machine from your Menu Bar (or from System Preferences). Choose Select Backup Disk. Select Seagate Backup Plus Drive (or the external drive as shown) connected to your Mac, and choose Use for Backup. Your external backup drive is now ready, and a Time Machine backup will start. The Seagate Backup Plus for Mac with Thunderbolt. Everything needed to transfer, store and backup files using Thunderbolt technology. Thunderbolt technology is a revolutionary interface supporting high-resolution display and high-performance data devices through a single port. At 10 Gbps, Thunderbolt technology is up to 20x faster than USB 2.0. Seagate Backup Plus Slim for Mac 1TB External Hard Drive HDD – USB 3.0 The stylish external hard drive MacBooks, Backup Plus Slim for Mac makes it easy to store and access 1TB of content on the go The perfect compliment to personal aesthetic, this USB drive features a minimalist metal enclosure.
It sounds as though it has failed.
I don't know if Seagate has a test utility suite for those on their website, but they often require windows to test their drives.
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If it is under warranty, then I would investigate further with their tools.
If not, others here may be able to offer additional troubleshooting.
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Are you using their bundled software at all? If so, try uninstalling it, then reformat the drive by using the Partition tab.
Whats a free video editing software. If you think it might be something on your Mac (or a problem with it), can you try the drive on another computer?