I am a Gemini woman. We like challenges, but we do not REALIZE it. If you really like her, then JUST LEAVE HER ALONE. She may come back, she may not. There will be no "what if" if you move on. You MOST DEFINATELY not win her by calling her or appearing "desperate." Bottom line is that as a Gemini woman, we are constantly changing our minds and are constantly looking for a "high." We (at least me) honestly do not mean to. I literally drive myself crazy b/c I don't know what I want myself. If you want to win her, you will have to understand that there are a few different personalities in her. We don't want doormats THAT IS FOR SURE. So whatever you do, stand your ground, be confident, COCKY even. Take control and don't put up with any of her fickleness. Here is the best way to put it, it is either YOU or HER. If you let it be HER, you just lost her.
And for your own sake, if you want to be with this girl, remember you will have to understand and accept and endure her different personalities at any given moment of the day, week, or month....FOREVER.