The second is correct because "do you think" is the inverted verb-subject that makes the sentence a question. "The reason is" is the object of the sentence; there is no reason to invert the subject and verb.
Americans frequently say the first and, similarly, use noun clauses incorrectly. For example, people sometimes say, "I wonder what is she going to do today?" But a noun clause ("what she is going to do today) is acting as a noun (subject or object) and, therefore, the subject-verb order should not be inverted. The correct way to say this is "I wonder what she is going to do today."