Why aren't the Biblical Apocrypha included in the protestant Bible? Biblical Apocrypha are portions of Bible that are printed in some editions of Bible between Old and New Testament, sometimes called inter-testament. When Martin Luther was translating Latin bible into German language, he left the translation to other people, and labeled it as "Apocrypha: These Books Are Not Held Equal to the Scriptures, but Are Useful and Good to Read".

My Question is, why are they not included in the modern protestant Bible?
These books of the Bible were accepted as part of the canon (part of the Bible). These books have been around for a long time. First of all, the books called apocrypha are related to the Old Testament. The New Testament is accepted with its 27 books among the major Christianity branches (Catholics, Protestants, Evangelicals).

The Old Testament Canon was taken from the Jewish Bible. The Jewish recognized an historical value to the apocrypha, but not one of authority. The Catholics started to view the apocrypha as part of the Bible during the counter-reforme in 1546 (Concile of Trente). Principally to object the protestant attack on particular doctrine like the purgatory. 

In fact, the protestants returned to the position of Jerome, who presented the Old Testament with the apocrypha separated to the Old Testament (Prologus galeatus) around 390.

--Source Magazine Theologie Systematique, Article : Apocryphes ou Deuterocanoniques by Henri Blocher. (Sorry for the French source) Here is the English transcript

Why are those books not included in the post-reformed Bible? Simply beacause for the Protestants these books were never part of the Old Testament. The New Testament does not quote them, as it does for most of the Old Testament. The Jewish people did not see those books on the same levels then the rest of the Old Testament Canon.