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-What are your ages?
-Are you male or female?
-What were the issues in the relationship that made her feel she needed space?
-Do you think there may be someone else?
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It sounds like she thinks you were dragging your feet about marrying her and she got tired of waiting for that commitment of marriage. What you need to do is to talk to her and tell her that you would marry her tomorrow if you could but you wanted to honor her parents wishes and that you are sorry that things ended up the way they did and then tell her that you will respect her wishes to have time to herself and that you just wanted her to know that you love her and will be there for her when she needs someone to talk to, if she knows that you are willing to give her time and care for her as a friend that might make her come back to you. You have to show her that you will wait by actually doing just that wait without being a pest and allow her to have that time alone. She may have felt like you took her feelings for granted because she never got that date or possibly a ring. Show her that not only are you her love but you can be a good friend also. If she loved you at all she will not just jump into another relationship because that would only be rebound dating and that never works out.
I would give her one to two weeks before contacting her again after that and then when you call don't talk about the relationship or getting back together talk about how she is doing, don't mention about missing her unless she mentions it first only talk about the relationship if she initiate the conversation. In time she will see that you are the best man for her but you have to be willing to work on getting her back which may mean doing as she wants and possibly getting married and you have to make sure you are willing to do that and want to do that. I would give her at least a month or two and then ask her if the relationship is over and whether or not you should move on with your life with out her, by then she will have had time to think about what it is she really wants and hopefully she will see that being back in the dating scene isn't that easy anymore. Just be patient and move at her pace.