It's horrible for someone to keep you hanging for so long. Have you spoken face to face or on the phone about what happened?
If you don't like this treatment, then you make the decision to end it . You are not unloveable. You are alloewed to make mistakes (or not -you haven't said what the argument was about) A good relationship is about how you get through the shit moments. That's both ways.
Are there other signs that it hasn't be good between you?
Give yourself closure and you are not unlovable sometimes arguments are recoverable sometimes they are a necessity to end an unhealthy relationship. It doesn't mean you are unlovable just that the current partner may not be what you need