First, I think it's vital to have regular performances, recitals, and other special events for students. Recitals motivate students to practice for several reasons. One is the fear of public failure, which can be quite a powerful motivator. But recitals also represent a very tangible goal, something for students to work towards. Without a performance goal, practice can feel aimless. Recitals and other performances (including auditions) keep students focused.
Recitals are also a great chance for students to get public recognition for their efforts, which powerfully reinforces their hard work. Which brings me to another valuable way to keep up students' motivation: recognizing their progress. Recitals and other special events are excellent platforms for recognizing students' achievements, but even in regular lessons teachers can take a moment to discuss with students (and their parents, ideally) how much progress they've made. As with any positive feedback, the trick to be honest and specific. Generic praise, like a meaningless "Good Job!" doesn't have the same impact as a specific "Your bow-hold has really improved the last couple of weeks" or "You play this phrase with beautiful expression." I know some teachers who videotape or record students over the course of a couple of lessons, so the students can hear or see how much progress they've made.
Finally, students often have more motivation when they have some control and some choices within a lesson. It's hard to have someone constantly telling you what to do when, especially for young teens. Instead, I offer students choices: "Would you like to play your scales or your etude first?" "Which piece would you like to start with today?" These simple choices let students have some say in how their lessons go, and that keeps their motivations much higher.