First, the specific reason: it's Gentleman Jole and the Red Queen. A frequent motivator to reread earlier books in a series is the acquisition of a new novel in the arc. And ever since I began reading a large percentage of my new-book consumption to the Kindle, I can add the release in e-format of earlier books in a series to that reason, as well.
The broader reason, though, is that my love for a book or a series is triggered by more than a story. I'd like to share those "more" elements that make a book worth re-visiting, whether it is once or twice, or on a regular basis.
CharactersIt's easy to fall in love with lovable characters; but I am also drawn to complex ones. They reward a re-read by revealing more of their nature each time I encounter them. I see additional facets of personality or motivation with each new reading. Villains may provide more appeal in this way than heroes, but in the Vorkosigan novels, it is Vorkosigan himself who is most complex. And if the latest novel in this series has little of Miles in it, I can still get my fix from the earlier books.
World-BuildingVorkosigan's world is political-cultural as much as science-fictional. Bujold shares that ability to create a tasty culture with another author whose entire multi-novel series I feel compelled to re-read each time a new one appears: C.J. Cherryh and Foreigner. But the world a writer builds may be the familiar one we live in, with a single element twisted in an innovative way. Sheri Tepper has done this with The Fresco and The Family Tree, and they are two novels I return to on a regular basis.
High ConceptThis is a harder element to pin down. I often do not know until several books into a series why one story-arc will qualify as re-readable and another will not, and the deep, broad, or delicious idea that recolors everything outside the novel for days after I read it is one. Tepper's novels have this, too—I need not agree with the concept to have it set hooks in my brain. Elizabeth Moon's Seranno and Vatta series qualify, for instance, with a cogent question. What changes would access to a real fountain of youth make in society?
There are other considerations, like "moral" protagonists (Honor Harrington or Harry Potter, for example, whose less-complex main characters embody the moral of the story), or quotable thoughts—anything by Rand or Heinlein is a goldmine for quotes, as are all of the Connie Willis novels. But the three above are sufficient to bring me back, again and again, to relive the joy derived from reading a good book.
Even when there is not a new book in a series-arc.