why we blow shofar in elul

The Pirkei d'R' Eliezer's explains why we blow shofar during Elul:

תניא בפרקי דרבי אליעזר (פרק מו): בראש חודש אלול אמר הקדוש ברוך הוא למשה: "עלה אלי ההרה", שאז עלה לקבל לוחות אחרונות. והעבירו שופר במחנה; משה עולה להר, כדי שלא יטעו כמו שטעו בראשונות במעשה העגל. והקדוש ברוך הוא נתעלה באותו שופר, שנאמר (תהלים מז ו): "עלה אלקים בתרועה, ד' בקול שופר"

Sefas Emes asks (in the likutim): if the purpose of blowing was to avoid falling prey to the same mistake of eigel worship that happened during the first 40 days, then shouldn't the shofar have also been blown during the middle 40 days Moshe spent on Har Sinai as well as the last 40?  We should be blowing shofar all summer!

He offers two answers.  The simple answer is that during the middle days Moshe went up to ask Hashem for forgiveness for the eigel worship.  Davening for forgiveness for cheit ha'eigel is itself a deterrent against a similar sin.

The second, deeper explanation is that the shofar is effective only during an eis ratzon.  Klal Yisrael felt a closeness to Hashem during Elul that they had not felt before, and they were able to use the shofar davka during that time period as an instrument to cement that connection and deepen it.  

Were I a baal mussar I would point out that we are speaking about the dor de'ah, the dor that stood at Sinai and received the Torah on 7 Sivan.  We are talking about a dor that had sinned with cheit ha'eigel, and knew that Moshe had to spend 40 more days on Har Sinai davening for their lives to be spared.  They as no other dor knew what closeness to Hashem means, and knew the danger the eigel posed.  Yet, they still needed a safeguard against making the same mistake all over again!   They still needed a shofar כדי שלא יטעו כמו שטעו בראשונות.