How one should rejuvinate my relationship with my ex girl friend?

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I often hear "some thing happened and after such a wonderful and long relationship we parted ways". In another situation - my friend says, " my ex girlfriend is living alone; she seems to be lonely." I some time ponder upon these questions - what happens to these relationships? Why do they become lifeless or less virile after some months have gone by?I meet my ex girl friend quite often these days - she has taken up a job in the same multi complex; she rides a scooter these days and we see each other at the parking stand. Last week end I was in a party and I saw her there. I came close and thought of speaking to her. I was rather shaky but my friend saved me from that uncomfortable situation. I want to rebuild this relationship. We had broken off on a triffle issue. I had requested her to come along with me on a vacation. And she had other ideas. Later I had seen her in a party gossiping with a new gentleman. And then I thought she took less interest in me and thus the gap between us started growing. But now what I see is different. The other day while hurring into the lift she turned her head over her shoulder and smiled at me. Now it appears she wants me to do some mending. Or may be I don't know - what is playing in her mind.