I taught English for a few years, and the last place I worked was an all-girls high school. One of the most common requests I got from parents was to get their daughters to read something new: "She just keeps rereading the same books, and they're not even on her level! How can we get her to move on?"*
Short answer: You wait.
Longer answer: Keep offering new books. Buy them for her; leave them around; read them yourself with a secret smile and tell her all about them...but don't push her too hard. She's rereading those books because she needs them, and who can blame her?
Being a kid is tough. Even walking down the halls some days can feel like going into battle. If your kids and students need to escape into a familiar fictional world at the end of the day then let them, and don't make them feel bad about it.
In fact, a good general life rule is to not ever make anyone feel bad about reading anything. They're reading for Homer's** sake! Stick with making them feel bad about tormenting others or eating your brownie when you weren't looking. Reading should be a guilt-free zone.
One student would only read Agatha Christie mysteries, which I actually thought was quite sophisticated for a 13-year-old. (This was of the era when a film starring Jennifer Garner as a young Miss Marple was rumored to be in development. My student was horrified.) She was at a new school, meeting new people and adjusting to a huge new workload. She wasn't ready for new books as well: Miss Marple and Poirot made her feel better, and I wasn't going to take that away.
Four years later I ran into her mother, and she remembered my advice to relax and wait it out. Her daughter did eventually move on to new books (of course), but she was slowly buying up her mother's vintage Christie collection so she could take them with her to university. And good for her, I say: there will be plenty of new experiences waiting for her there and it's only right that her old friends should be along for the ride.
My security character is Adrian Mole. I've read every title starring Sue Townsend's brilliant creation many times, and those are the books I reach for when I need comfort. In 2011 I was in an earthquake in Christchurch and got stuck in the city overnight. The ground kept shaking and, knowing I would never be able to sleep, I downloaded Adrian. He got me through.
What are your security books?
*Yeah, that's a pretty good teaching/parenting problem to have, isn't it?
**Homer the poet, not Homer Simpson. OBVIOUSLY.