Time machine can not backup with no visible reason

Formatting in disk utility then running Time Machine should work for backups.

It’s just something to try. Usually, formatting before a backup fixes things.

I'd suggest before reformatting the disk, which will erase all data on it, that you attempt to repair it in Disk Utility first. To do this, open Disk Utility and for best results, choose View > Show all devices, (or press Command-2) and run first aid on the top level external disk and all volumes below it. Note that this process can take some time depending on the size and composition of the disk and its volumes.

HTH

Thanks for this. I'm pretty sure the same thing happened to me. I got a Western Digital hard drive in 2016, and at the time it worked perfectly on my mid-2013 MacBook Air. At some point in the not-so-distant past however, the drive went into "read-only" mode somehow and I couldn't do much of anything with it. A sighted tutor and I attempted to troubleshoot this recently. My theory is that he inadvertently made the problem worse. He doesn't think too highly of Apple, but is very good-intentioned. He and I always listen to music on my Mac, and whenever he's on here we shut off VoiceOver completely.

On occasions I have found that removing the drive as a Time Machine destination and then adding it back again can resolve issues such as this.