Shofar Source

Rav Hamburger told me this minhag is found in many old sources, see Minhogim Dvei Maharam Merotenberg (סדר ריינוס לערב ר"ה), Hagahot maharil which is also brought in the Darkei Moshe (סימן תקפ"א), Minhogei Worms (Kirmum, from the time of the Levush) and many other books. The reason given for the stopping (in Minhagei Maharam) is:
ומה שאין תוקעין ג' ימי' לפני ר"ה כדי שלא יהא המזיק מורגל ל' יום רצופין ואז אין יכולין לערבנו ולהבהילו, אבל כשחוזרין ותוקעים ביום הדין אז נרתע מלקטרג
I think the explanation is, if we would continue on RH and have only two days brake, there would be 30 days altogether,and then the Tekios would not be Mabalbel the Sotton at all. (But since Elul is always 29 days, maybe two days brake would have been enough, וצ"ע).