[Solved!]
I had exactly the same problem - no matter how many times a I rebooted my Mac or reformatted my WD drive, the first Time Machine backup would succeed and any subsequent one would fail with “Error occurred while creating the backup folder”. It took 3 calls to Apple Support, but they have solved it for me. I had my first complete backup yesterday, and about 20 successful hourly backups since then.
My setup: A new (2019) MacBook Pro 15" running Mac OS Mohave (10.14.5) with a new 4TB WD My Passport.
Steps Apple Support took me through to fix this:
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Get into Repair mode by powering down your Mac, then immediately after pressing the Power button to turn it back on, press and hold Command-r (⌘+r) for a while, until the Mac does NOT show a booting scroll bar, but instead asks you a question or two like “Language?” Note you must power down, not just Restart, since you can’t do Command-r fast enough during a Restart.
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Once in Repair mode, you will be shown a list of 4 choices. Select Disk Utility. It looked to me like the same Disk Utility you could get at without Repair Mode but you have to be in Repair Mode.
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Select your primary disk (usually Macintosh HD) and click on First Aid. For me this took 4 minutes and ended with a green check mark that everything was fine. I don’t know what you should do if your results vary.
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Select the External WD disk you want to use for backup and click on Erase Disk (presuming you want to use the entire disk as your backup - if not you’ll need to call Apple for different directions). Pick a name and you want to format as “APFS” (not encrypted or case sensitive) with GUID Map. That was very quick.
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With the external WD drive still selected, click on First Aid and say OK to erase disk. This was also very quick and also ended in a green checkmark. Again, if your results differ, talk to Apple.
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Exit the Disk Utility and reboot.
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Start up Time Machine, remove your existing backup disk selection (especially if it is the disk you were just erasing), and re-select the external WD disk you just did First Aid on as your backup disk.
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Let the first backup complete. Wait for a while to confirm that subsequent backups have also completed successfully. I waited 24 hours and when I went into TimeMachine there were about 20 successful hourly backups waiting for me.
I asked why First Aid would solve the problem, and was told First Aid was not just a checking tool, it also silently fixes minor incompatibilities. Whatever the issue is that Apple + WD have do get fixed by First Aid. Note that we ran First Aid on both the Apple internal drive and the WD external drive to get them into the same state. Minor point of interest - my internal drive is encrypted, but my external drive is not. Before the First Aid fixes, I was getting a warning about this. I no longer do.
I hope this helps everyone else on this thread.
Mark Batten-Carew