Probably every tour guide who visits the site of Qumran makes note of the fact that a portion of every Old Testament book was discovered in the nearby caves with the exception of Esther (given that Ezra-Nehemiah were a single book). You may have heard a suggestion or two offered for this lack, but I found helpful a summary of possibilities given by Sidnie White Crawford in her article on the Book of Esther in the Encyclopedia of the Dead Sea Scrolls (1: 269).
1. The fact that no fragments have been preserved is simply owing to accident or chance. The book is relatively short and may have been in existence in the community but simply not preserved or discovered.
2. The male community at Qumran was not interested in a book in which the hero was a female.
3. The Qumran community was opposed to the book which describes a Jewish woman marrying a Gentile king and not following the Jewish laws.
4. The book of Esther was not known in the land of Israel in the first century.
5. The book was written too late to be included in the body of sacred scrolls.
I would be inclined to believe that because of #2 and #3, #1 is true. It may also be observed that the book of Esther is never quoted in the New Testament, nor is Purim mentioned.