Machine is running Win81 64, and is installing updates OK. No other issues with the machine currently observed.

DISM /ONLINE /CLEANUP-IMAGE /RESTOREHEALTH takes about 20 minutes to fail in the way described in the title. The longer description beneath the error code says that the source files could not be downloaded (the machine has a working Internet connection and is using Windows Firewall and Defender).

In the DISM log, it says:

Code:
[2360] Caller did not request sparse mount
[2360] Mounting new image.
Wim:         [\\?\GLOBALROOT\device\harddisk0\partition5\Recovery\WindowsRE\Winre.wim]
Image Index: [1]
Mount Path:  [C:\WINDOWS\TEMP\45ec7f06-e19a-4a81-bceb-07e25030e617]
[2360] Wimserv process started for guid a94c33c9-2093-48f4-98c6-94e0f60753bc.  Id is 2400
[2400] ImageUnmarshallHandle: Reconstituting wim at \\?\GLOBALROOT\device\harddisk0\partition5\Recovery\WindowsRE\Winre.wim.
[2400] Mounted image at C:\WINDOWS\TEMP\45ec7f06-e19a-4a81-bceb-07e25030e617.
[2360] [0x8007007b] FIOReadFileIntoBuffer:(1415): The filename, directory name or volume label syntax is incorrect.
[2360] [0xc142011c] UnmarshallImageHandleFromDirectory:(511)
[2360] [0xc142011c] WIMGetMountedImageHandle:(2568)
[2360] [0x8007007b] FIOReadFileIntoBuffer:(1415): The filename, directory name or volume label syntax is incorrect.
[2360] [0xc142011c] UnmarshallImageHandleFromDirectory:(511)
[2360] [0xc142011c] WIMGetMountedImageHandle:(2568)
[2360] ImageUnmarshallHandle: Reconstituting wim at \\?\GLOBALROOT\device\harddisk0\partition5\Recovery\WindowsRE\Winre.wim.
[2360] ImageUnmarshallHandle: Reconstituting wim at \\?\GLOBALROOT\device\harddisk0\partition5\Recovery\WindowsRE\Winre.wim.
[2360] ImageUnmarshallHandle: Reconstituting wim at \\?\GLOBALROOT\device\harddisk0\partition5\Recovery\WindowsRE\Winre.wim.
[2360] ImageUnmarshallHandle: Reconstituting wim at \\?\GLOBALROOT\device\harddisk0\partition5\Recovery\WindowsRE\Winre.wim.
[2360] ImageUnmarshallHandle: Reconstituting wim at \\?\GLOBALROOT\device\harddisk0\partition5\Recovery\WindowsRE\Winre.wim.
[2360] ImageUnmarshallHandle: Reconstituting wim at \\?\GLOBALROOT\device\harddisk0\partition5\Recovery\WindowsRE\Winre.wim.
[2360] ImageUnmarshallHandle: Reconstituting wim at \\?\GLOBALROOT\device\harddisk0\partition5\Recovery\WindowsRE\Winre.wim.
[2400] Received unmount request for image with guid a94c33c9-2093-48f4-98c6-94e0f60753bc.
[2400] Unmount for image at C:\WINDOWS\TEMP\45ec7f06-e19a-4a81-bceb-07e25030e617 complete.
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The last line is basically entirely oriental characters, which files up the rest of the file. I get the same result every time I run the command.

chkdsk /f /v /r turned up nothing indicating hardware failure (such as read failures, bad clusters found).
sfc /scannow was failing but since I fixed an issue (relating to the fact that the pagefile had been switched off), that now says that no integrity violations were found.
I also ran a DISM command with /startcomponentcleanup, which finished successfully.

I cleared out C:\WINDOWS\TEMP, but that hasn't helped.

The automated maintenance system was also broken (the task scheduler entries for it were simply missing, I restored them from another Win81 machine and since then I manually ran the automated maintenance through Action Center and that worked fine.