@LiveYourDream has rather accurately captured the mental gymnastics she likely went through which led to the asking for time.
@Glassguy has re-engaged, which seems well received, although she may have questioned it as compared to his previous behavior.
This seems to have already resolved itself but I have a couple of thoughts that might be of some use.
This lady is 29. Her clock may indeed be ticking but she's still young insofar as self awareness and wisdom is concerned. She hasn't yet figured out that the fact that a man is taking the time out of his life to reach out means defacto that he likes her. OK.
I agree he probably came off too cool & aloof and that she pulled back thinking he didn't like her. However this stage of things is tricky to navigate because she will be trying to reconcile the perceived (from her view) change in behavior, and may wonder will the real Glassguy please stand up.
And there is the possibility that there is someone else she is seeing too, or may have just met.
Add to that work schedules, childcare schedules, and life in general and you get this cat and mouse thing. When that happens it's best to go with the flow and see what she does.
You asked her out, and asked her for a specific time now twice since re-engaging. If she didn't respond or if she can't seem to get you a time and place for getting together then perhaps it has in fact run its course.
Going forward if you want something more meaningful than pump & dump then the best way to date someone who you really like is to be completely outcome independent. That is to engage and enjoy the time that you have together, but to also understand that each time could be the last time you see each other unless there is some defining conversation; she seemed to be pushing before for such a conversation, but not now.
Assuming it is over with then just take the wisdom here in this thread and file it in the back of your mind.
It is hard to do but people cannot carry around the pain caused by person A, and withhold connection from person B because of what person A did. It had nothing to do with person B whatsoever. It takes some time in life to get to the point where you can allow yourself to feel and to connect without all that past baggage. It can be tough. But if you want a successful connection with another human being you are going to have to let your guard down emotionally at some point. So that will be your takeaway lesson in any case.