A common complaint about reading to little kids is that they want to read the same books over and over. It's true, they do. I've brought kids to bookstores and seen them zero in, unsurprisingly, on the books they already have at home. Kids find comfort in the familiar, of course, but I think there's more to it than that. Books they already know provide great scaffolding for them to discover new things their brains can do.
I'll use an example with which I've become very, very familiar: reading Goodnight Moon to A, aged 18 months. On our earliest readings, she rarely let me stay on a page long enough to finish it (and they aren't exactly wordy pages). The only exception was when she was so glassy-eyed that she wouldn't have moved a muscle if I'd tried to read her the complete works of Shakespeare.
But since then, she's transformed into a much more active listener. She usually selects the book herself now, and once we get started, she participates. She always tries to say "balloon" when we get to the red balloon on the first spread, and she makes sounds for many of the animals referenced. (I never realized just how many animals are in even picture books that don't focus on them until I sat for A, who does a rollicking "roar" and a mean "meow.") My personal favorite, though, is when we get to the page with "the old lady whispering hush," and A puts her finger to her lips and says, "Ssshhh."
After a first read-through, A will often take the book and leaf through it herself. Watching the way her eyes take it all in, I could swear she's literally reading.
So yes, I often end up reading the same book to the same child. But as long as she keeps making new discoveries, each reading will be just slightly different from the last for both of us.