who approaches the king in the inner court without being summoned—that he be put to death: The king's guards strictly controlled access to him to prevent unwanted guests from wasting his time with minor requests. These were the official court rules, so Esther faced great danger. She likely decided against asking for an audience through a messenger, possibly because she would have to explain her reasons.
I have not been summoned to appear before the king for the past thirty days: Esther had no guarantee of his favorable response.