Girlfriend breaks up and says it was not serious

My partner (24F) and I (24M) have been together for two years. We are having a long distance relationship. We’ve broken up three times already. But these are not normal break ups. It was one moment of break up.

During the last incident, I was already upset with her, so I wasn’t texting much. We had have an arguement, context of it is not important here. When she came back from work, she didn’t text me either. I didn’t ask “where are you” or “are you okay” like I normally would—I just texted “good night.”

This morning, she woke up and texted me: “You don’t care about me, you don’t have a heart, you don’t think about me. F** off. Don’t text me back.”*

The thing is, I was the one who was mad, and I was waiting for her to make a move. But instead, she flipped it around. We talked immediately, she implied breaking up. I told her that speaking in this tone is damaging and emotionally exhausting, and she said I didn’t “understand the bargain.” I asked directly) she loves to imply breaking up), “Are you breaking up with me?” and she said yes. We talked why, why she felt that way. I asked I mean. She said she didn’t see the care she wanted. Then we said take care. I ended up the relationship there in my mind. I have blocked here and then she texted me in 10 minutes. Told me that I was waiting for it, I didn’t want to try to convince her. Things like this, I didn’t step back. So she came, she said she is sorry. She wasn’t aware of what she was doing. She said she didn’t understand the consequences, she wanted to go away a bit for couple of hours. Its her excuse.

This was my red line—because we’ve gone through the exact same situation two other times in the past two years. And every time, right after she said that it’s over, she tells me she didn’t really want to break up. She says she just wanted me to care more, to chase after her, to make a move. Wants me to try. But what I am saying is there is nothing to try. She wanted to see where are you messages when she woke up. And she broken up because she didn’t see ditgose messages instead she saw a good night message.
She says she loves me too much and doesn’t actually want to leave. She says “How can I want to leave you while I am in love with you that much.”

We had already talked about this before, after the last two incidents. She agreed that this was toxic, and promised not to do it again. But now she has done it again—over nothing.

Now she’s telling me she understands how serious I was this time, and that she won’t do it again. The other two was this much serious btw, not less. I told her I need some time to think. The truth is, I’ve already thought about this dozens of times. I had decided that if she did this again, I would end the relationship—because it’s too painful, and I don’t believe she will change. But she talked too much and made me think if I am overreacting. That’s why I wanted some time.

At the end of our last conversation, I said we should wait a couple of days while I think. She agreed, but then added: “Think about this too—what if this girl kills herself if you break up?”
This was the first time she is telling something like this.

I honestly don’t know what to do or what to think anymore. In this relationship, I thought we are the best couple, we are the perfect match and we are made for each other. What I think is she can not prevent this to happen. She will break up and then say she was not meaning it. As I said before, I was expecting her to do this and she did. Now 2-3 hours passed. Memories are coming to my mind. Yes I was saying I should break up if she does this again but after 2-3 hours it made me soften. Its my character btw. Time takes away everything. Yeah I dont know what to do.

TL;DR
My girlfriend breaks up and when I take it seriously she says she was not serious. She says she broken up so I move to her, try to give her back. This happened 3 times in two years and I said we will actually breaks up if ever happens again and it happened today. Now she told she can kill herself. Not emphasized, but just told. What should I do?