What do I do with this situation?

Me and my girlfriend have been going through a rough patch lately. We kept on just tryna one up eachother and nitpicking every little thing, it culminated in a big argument where we very nearly decided to just end it. I put forward that I was willing to try with her. She said something along the lines “I’m willing to try, but this will be the last time. On one hand I want to go our separate ways because I don’t think it’ll work but on the other I want to try” she also said she “doesn’t feel the same connection, don’t know where or why it’s gone”

other information to consider is that the little one upping eachother was the last week or two. We’ve been together since January. And there have been times before where we’ve nearly broken up.

my underlining question here is where do I go from here. On one hand she was given the opportunity to end it quite peacefully, or try again. However she explicitly states she doesn’t think it’ll work which is not an attitude I’m awfully confident putting my side of the effort towards.

Any advice which could assist in what I do from here is appreciated
What do I do with this situation?
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