Most Helpful Girl
Let her know that you really don't appreciate these constant threats that she'll break up with you. Just straight up tell her that if she continues doing that, she'll be surprised one day when you take her up on the 'offer' and you'll be the one to walk away.
(that's pretty much what my boyfriend said to me when I went through a phase of also saying I felt like a breakup was the only real way we could resolve our issues. needless to say, that shut me up really quick.)
Most Helpful Guy
her actions is waaaay more powerful than what she's saying. she hasn't broken up with you yet.
of course the typical generic tell her how you feel is the start and let her know you are not going play pendulum with her when comes to her emotions. if she can't control it and she threatens the relationship then no ones making her stay. this relationship was built out of sacrifice, selflessness and trust not just 100% of her emotions.
you gotta lay down the law is all im saying.