The problem with "unputdownable" is that it makes "to putdown" the verb. I'm just putdowning this book. I putdowned it after a couple of hours. "Unputtable" makes more sense as a word, but you need the "down" to get the phrase to work. Unputtable-down? Undownputtable? Downunputtable?
And now I'm wondering what I would consider unpickupable.
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