I think so. The French sentence is a bit weird, as if it could be about a very long book that you need to read in many sessions, as well as to a book you are reading many times. The latter case is a more intuitively plausible context and yet, it would be much more natural to say "Relis le livre encore et encore".
Your 'over and over again' would assume re-reading the same book many times, right? Anyhow, that's the only down side i see to it as a translation for this french sentence
Well, it's not completely off the table in the french sentence. 'relis' would be much preferred in that case, but you can stretch contexts to make it work the other way too (especially if it's not a book you read from one end to the other, say book with many independent parts put together, or a teachings book. The dictionary would be a good example, a lot of people have read many parts many times, yet very few have read every single line in it at least once. So they can't really "relire" the book as a whole, technically, yet they can do the 'reading it' 'over and over again')
The main point is: that sentence is a bit strange