Is there something in Sirach that caused it to be considered Apocrypha? My limited research on the topic suggests the only reason Sirach (or Ecclesiasticus or Ben Sira, etc.) was put in the Apocrypha was because the Jewish canon excluded it.  As for why the Jewish canon did not include it, I couldn't find any reasoning that involved the content of the book.

Is there something theologically problematic in Sirach that prevents it from being classified as Scripture (from a Protestant view)?
William Whitaker's Disputations on Holy Scripture is a classic Reformation-era work that goes into great depth regarding the reasons that the apocrypha were rejected.  He deals with Sirach (Ecclesiasticus) beginning on page 90. 

He begins by arguing that the "common" reasons for rejecting the apocrypha also apply to this book, such as not being part of the Jewish canon, lack of early acceptance, and a lack of an original Hebrew version.  He also notes a number of deficiencies, such as the author seeking pardon for his translation:


  He asks pardon, if he should seem in some places to fail of an adequate power of expression. By all which he sufficiently proves that he is neither a prophet nor endowed with a prophetic spirit.  For the Holy Spirit asks pardon of no one, hesitates not in the choice of words, and ever reaches the mark he aims at.


But Whitaker focuses on the book's explanation of the events of 1 Samuel 28, in which Saul, following Samuel's death, goes to a medium in an attempt to speak to Samuel's spirit.  Sirach 46:20 reads:


  Even after he had fallen asleep, he prophesied
  &nbsp;&nbsp;&nbsp;&nbsp;and made known to the king his death,
  and lifted up his voice from the ground
  &nbsp;&nbsp;&nbsp;&nbsp;in prophecy, to blot out the wickedness of the people. (NRSV)


Whitaker contends that "the souls of the saints cannot be evoked by magical arts or incantations," and notes that in several places Augustine argued that Saul rather spoke with a mere "phantom and imaginary illusion produced by diabolical devices."  Thus Sirach 46:20 is in error and cannot be scripture.

Other Protestants have raised issues with other portions of the text, such as Sirach 15's discussion of free will. E. J. Young also writes:


  Ecclesiasticus and the Wisdom of Solomon inculcate a morality based upon
  expediency. [...] Ecclesiasticus teaches that the giving of alms
  makes atonement for sin (3:30). ("The Canon of the Old Testament" in Revelation and the Bible Contemporary Evangelical Thought)


It's not clear to me, however, if such issues with the text were raised during the Reformation.  Martin Luther did deal with Sirach 15 is his Bondage of the Will, and, though not accepting the book as canonical, nonetheless contended that it did not say what Erasmus argued. (see §46ff. of Bondage of the Will, and The Reception of the Church Fathers in the West, 584 for a summary)

So we can safely conclude that while Sirach was excluded primarily for the more general reasons the apocrypha was rejected, it was nonetheless found to have at least some theological issues in itself.