Ultimately it is up to her, but there might be some things you can do to encourage her to stay. I always think my happiest au pairs are those who have other stuff to do. Our current au pair has joined a local gym, and signed up for language lessons, and made some local friends, so I am feeling pretty relaxed about her staying! Does she have any interests that you could encourage her to follow? Eg: if you can afford it and are fond of her, you could sign her up to a short local course in drawing or pottery or something. And be nice to her (not that you wouldn't) and be patient and understanding. Breaking up is horrible, and I'm sure she'll appreciate you being there for her. I used to make my friends a small 'break up kit' with a magazine and chocolate and bubble bath. Perhaps she would appreciate that, depending on what kind of relationship you have.
Remind her to do what's best for her but also say that you're really enjoying having her, kids love her and you'd really really love to have her around. Maybe also suggest contributing to some things she can do? A class, club or hobby, perhaps? Something to take her mind off it rather than bribe her to stay iykwim
Also 2nd the break up kit option. Maybe see if there's a website that ships things from her home country, offer to get her her favourite chocolate or something. If not get to town and buy her some bath bombs a few magazines, maybe a book and some chocolate. Try to be there for her rather than "pull yourself together and work". It'll work a lot better. She may still leave anyway but it's more likely she'll stay if you're kind and considerate to her imo.