If you use Sync, best is to disconnect Sync temporarily during troubleshooting.

This could be a problem with the places.sqlite and favicons.sqlite files in the Firefox profile folder.

• use the "Places Database" -> "Verify Integrity" button on the "Help -> More Troubleshooting Information" (about:support) page

If errors are reported with "Verify Integrity", close and restart Firefox or reboot and retry.

If "Verify Integrity" cannot repair places.sqlite, rename/remove all places.sqlite and favicons.sqlite files in the Firefox profile folder with Firefox closed. Firefox will rebuild places.sqlite and restore the bookmarks from the most recent JSON backup in the bookmarkbackups folder.

• keep a backup copy of places.sqlite in case a new places.sqlite database has to be created
• you lose the history when a new places.sqlite is created

You may have to restore an older bookmarks backup in the bookmarkbackups folder via the Bookmarks Manager (Library).

• Bookmarks -> Manage Bookmarks -> Import & Backup -> Restore
• https://support.mozilla.org/en-US/kb/restore-bookmarks-from-backup-or-move-them

See also:

• https://support.mozilla.org/en-US/kb/fix-bookmarks-and-history-will-not-be-functional
• https://support.mozilla.org/en-US/kb/cant-add-change-or-save-bookmarks

You can use the button on the "Help -> More Troubleshooting Information" (about:support) page to go to the current Firefox profile folder or use the about:profiles page (Root directory).

• Help -> More Troubleshooting Information -> Profile Folder/Directory:
  Windows: Open Folder; Linux: Open Directory; Mac: Show in Finder
• https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data

"Sort by Name" still works for me. Remember it is a single sort action and does not apply for new bookmarks.

Does it still happen in Troubleshoot Mode?

Thanks, Verify Integrity did not report any problem. I have sorted another folder on another, synced machine, it replicated to the failing one, and since then sorting is working again. Just before I would follow your solution to the next point.

"Sort by Name" still works for me. Remember it is a single sort action and does not apply for new bookmarks.

Just added the bookmark of this topic to a folder for testing, and instantly was able to sort it by name. Now it works well, thanks for the suggestion!