Arguments are normal, learning to "fight fair" is a required skill for couples. It leads to swifter conflict resolution and good communication skills.
You are not describing that though, you are describing scenarios where the person who supposedly loves you goes out of her way to tear you down, bit by bit, you're describing someone who does not stop until she's torn you to shreds and makes YOU feel guilty when you've had your fill and reached your breaking point.
That's in no way healthy, you are being stripped of respect, dignity, pride, and your very self-esteem.
Next time she threatens to leave, pack her bags and let her, then disconnect your phone.
You can't stay with someone out of guilt and pity, but if you do want to make a go of it, you can always drop her an email saying you'd be willing to consider reconciling once she's got a grip on her shyt.
There's absolutely no shame in looking out for yourself. Its actually important for us to do so.
Ps. I may sound callous and unsympathetic toward your gf, but it took my bf walking away from me to actually realize how horrid I had been to him. That prompted me to get help and work on myself, and I'm not mad at him for saving himself. He did the right thing, for both of us. These days our relationship is as strong and healthy as ever.