I don't believe the doctrine of "sola scriptura" in the sense that this term is used by many today and neither did Martin Luther.
Please notice his appeal to both the "testimony of Scripture" and "manifest reasoning" when he was ordered to disavow his beliefs at the Diet of Worms:
Your Imperial Majesty and Your Lordships demand a simple answer. Here it is, plain and unvarnished. Unless I am convicted [convinced] of error by the testimony of Scripture or (since I put no trust in the unsupported authority of Pope or councils, since it is plain that they have often erred and often contradicted themselves) by manifest reasoning, I stand convicted [convinced] by the Scriptures to which I have appealed, and my conscience is taken captive by God's word, I cannot and will not recant anything, for to act against our conscience is neither safe for us, nor open to us.
I find it interesting and instructive that this translation of Luther's words refer not to "reason" as such but to "manifest reasoning" or what we might call "clear thinking." Whether or not Luther had this distinction in mind, for us it opens the possibility of seeing both sides of this debate as talking past each other.
Those who reject "human reason" apparently think of it substantively whereas those who affirm it view it methodologically.
This is why those in the first group think that members of the second are arrogant and that those in the second believe that members of the first are ignorant. Given their different understandings of "human reason," each group is right. But if the measure is how well each group undersands the other one, both groups are wrong.
Sadly, this debate will never end until both groups realize that they are using the term "reason" differently.