boot - Folders disappear every time Windows XP starts up

Symptoms:

Whenever my Windows XP machine starts up, subfolders disappear from the first top-level folder, listed alphabetically (eg. from "C:\AA Backups"). The first time it happened I suspected user error (such as an unintentional delete or copy). But I then found it happens on every start-up, sometimes affecting huge numbers of files.

What I've tried:

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  Renaming the affected folder (e.g. to "ZZ Backups") just means that a different folder is affected the next time.

  
  


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  Avast found no virus or malware that would seem to be responsible.

  
  


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  The missing files are not visible to an undelete utility such as NTFSUndelete.

  
  


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  Running chkdsk/f found no problems and did not fix the problem.

  
  


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  File permissions also appear corrupted – a few files which should be accessible are missing "read" permission.

  
  

What's happened to this machine?