That's one reason I've been a constant advocate for self-selected reading. I know that students will not enjoy reading if they are not given the opportunity to choose their own stories and subject matter.
Hoggatteers will soon be reading books with the goal of stamina. One way we'll do this is through an iPad app called Epic! It's an app that hosts thousands of ebooks for kids to read. My nine- and ten-year-olds are perfectly centered for the books they can choose on this app. For those who are reading a level or two below grade level, they may pick books closer to their own reading levels. This is an app parents may subscribe to for a fee, but for educators, the subscription is free. With fiction and non-fiction selections, every student should find something of interest.
Some of the coolest features of this simple app include the ability for students for personalize the look of their screens - but only after they have earned those features. They can change their avatars, the background colors, the frames around their avatars, and more. Students may also label their favorite books and keep them on a special "shelf" to possibly reread at a later time. In fact, they may make quick reviews for the benefit of others who might be looking for a book to read.
There are many reasons for adopting this in our classroom, but the possibility of increasing stamina is my primary goal. The program, also available on a browser, tracks the time spent within a book, the number of "page flips", and books completed.