Many young children who are being read to, prefer to read the same book over and over again. If you are not living this out right now, you most likely remember how you were on your umpteenth reading of George and Martha, (or something of the like) and you would give anything for your child to pick ANYTHING else off the bookshelf for you to read. Turns out those little tykes had something there.
"When Mama Reads to Me" - Be There Creative Works on BeThereBedtimeStories.com
One strategy teachers use in classrooms from kindergarten to 12th grade is repeated readings. This is a research proven strategy that allows students to build reading fluency which leads to reading comprehension. Reading fluency includes the usual suspects of reading accurately and at an appropriate rate. But it also includes cadence (rhythm), tone and expression. Reading aloud is a sophisticated skill and students learn to master all these things while being read to and also being allowed to read passages or books over and over.
Having your student re-read passages allows them to eventually master all of these components of fluency. The next time you are reading with your child, ask him/her to re-read a section. You could even read it to them and model fluency for them. When they re-read a passage, it gives you the opportunity to point out what they did better the second time through. Everyone likes instant gratification and that will build their motivation to work on their reading, no matter what their level of expertise. Try it and let me know how it goes!