Every time I reboot, I get a prompt asking for permission to install
"Microsoft WPD FileSystem Volume Driver", every time I do, and all is
well until the next reboot.

If I choose "Ask me later" my card reader doesn't work, so it appears
likely that I do want this driver installed.

Any clues why I'm prompted on each bootup for the same driver?

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You can get more with a kind word and a 2x4 than just a kind word.