I would give her up. It is likely that there are many other reasons she broke up with you that she's not telling you, and this mystery thing is either the straw that broke the camel's back or the most concrete thing she could think of as a justification. There are no doubt many, many more reasons, many of which I doubt she even can concretely describe herself... it just feels wrong to her. If she seriously wanted you to change, she would've brought it up much, much earlier in the relationship and you could have had an honest discussion about it. But she didn't, and now you're surprised and somewhat hurt. That's love for you.
The question you have to ask yourself is what have you learned from this? Was she right about you being distant? How could have better communication on your part improved the outcome? I suspect the relationship is pretty much done for, and you should use this experience as a reason to grow as a person. The question to ask yourself is not, "How can I change to make her love me?" but rather, "How can I change to make myself a better person?" regardless of whether she loves me or not.
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