You are obviously dealing with a manager on the move, although much of her movement appears to be away from you. On the one hand, she is displaying none of the behaviors of today's best managers, particularly in terms of being available, accessible, and responsive. At the same time, and this might be a surprise, you are part of the problem.
Whenever you want to meet with her, all she has to say is that she'll get back to you, and you go away. You have rewarded her evasive behavior, so she is likely to repeat it. She may even believe that the problem or situation you would have presented to her has been solved, so there was no need for the two of you to meet. And she may apply this thinking to the future as well.
If you want to have more direct contact and communication with her, you need to be more assertive and persistent. If you just roll over, she'll roll by. The next time she says she'll get back to you, thank her and ask what time works best for her. If you can give her an idea of why a meeting with you is worth her time, she will be more likely to think that it is about time for the two of you to meet.
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