I have a problem with that kind of thing too. A girl shows interest, you reciprocate, her interest stops. However, interest is not a constant and it comes in degrees. It can change and it can be there but be insufficient to lead to a relationship. In such a case, one needs to let go, which is difficult.
Basically, I don’t know what’s wrong with women, but this mechanic is all too common (I’m talking about extremes, mild forms have always been there and are natural for everybody to some extent). I wish it were not there (or were contained to reasonable degrees and controlled by reason). But given that it is there, one needs to take it into account in “calculations” concerning one’s future and one needs to have a sober grasp of reality. If the interest is not there as a matter of fact, then it’s better not to have delusions, and to move on and find someone who will react in a normal enough way or who will be able to be worked on (everybody is a work in progress and some people can be worked on with good results).
People need to involve their reason and their will more. Even at the “dating” stage, things can’t be based on the momentary state of butterflies. Sure, there will be moments and there will be moods, but there’s a reason we have a judgement and a will, and receive education and formation. There must be some choosing and some mature act. Actions of a person playing in the field can’t be such a sinusoid as human sensations can be, there must be some reign of it by the person acting. Sorry for the jargon.
I’ll be praying for you and I hope the girl soon comes to her senses or you get the ability to move on.
The silent treatment, running away, the “now I’m here and now I’m not” are not acceptable behaviour and do not be deluded into thinking they are. However, they are common and no one is totally immune to such a tendency. Therefore you must be understanding if she comes to you and tries to talk like an adult person and get a grip of it. But if she’s lost in the game, then you can’t build a relationship with her. This does not mean she’s a bad person or a child in all areas of life, but it does mean she’s simply not ready for a relationship.
As a side note, avoid expecting too much from people you’re interested in. If you’re the initiating party, your interest will generally be higher and you can’t expect the other person to return all your interest immediately. Therefore it may happen that at this or that stage in life, you’re interested in a woman “that way”, whereas for her you might be a mere acquaintance, in which case she understandably won’t get out of her way much or give you a high priority. However, there are certain basic rules of politeness and certain aspects of kindness that oblige everybody and once she gets into more personal relations with you, the attention and priority must adjust accordingly. If not, then well, the relationship is a bit of a cold one.