hi Dumbstruck, i want to join
Learning_curve74 and say

breakup threats tend to be something a person uses when they are highly stressed, either as a means of getting their way, or theyre overloaded and need to escape the situation.
i used them frequently, myself, with my ex

its something you will want to nip in the bud; breakup threats erode trust over time.
im not sure id approach it from a boundaries context, at least if boundaries mean "holding her to" the breakup. if she feels that she needs to beg for you back each time, at a certain point, shes less and less likely to do so. in addition to what ill add below, you want to create a very soft landing for her.
the key is really in working together to get on the same page, if possible, on the fact that breakup threats hurt you, hurt the relationship, and to seek other (more constructive) ways...other ways, for her personally, to communicate her stress, other ways for the two of you to handle conflict, other ways to take a time out when things have gone overboard.
it will take some time and effort. it will be a conversation that needs to be revisited probably many times, and it will be something you need to approach in a benign and benevolent, and patient, way.
tell us how these things tend to go. whats the last thing she broke up with you over? what happened? what was said?