Elul: self-aroused teshuvah endures forever

הרמז לאלול אני לדודי ודודי לי.

The hint for Elul is, "I am for my Beloved, and my Beloved is for me."

The initial letters of this verse spell "Elul," signaling that this month is about a person first turning to Hashem, after which Hashem turns back to him.

כי בזמן הזה נתעוררו בנ"י בתשובה וזכו במעשיהם לעורר עת רצון בשמים כמ"ש מה הראשונים ברצון אף אחרונים ברצון.

For at this time Bnei Yisrael awakened in teshuvah and merited, through their deeds, to arouse a time of favor (eis ratzon) in Heaven, as it is said, "Just as the first [tablets were given] with favor, so too the last with favor."

Historically in Elul, after the sin of the eigel, Bnei Yisrael did teshuvah and earned the second luchos in an eis ratzon — the favor for the second set had to be aroused by their own efforts.

וזה נוהג בכל שנה ג"כ כי בפסח ושבועות הי' מתנות שמים כמו שהי' אז ביצ"מ ומתן תורה.

And this applies every year as well, for on Pesach and Shavuos there were gifts from Heaven, just as there were then at the Exodus and the giving of the Torah.

Pesach and Shavuos bring down free Heavenly gifts each year, mirroring the unearned redemption and revelation of the original Yetzias Mitzrayim and Matan Torah.

וע"י שלא הי' בזכות ישראל לכן לא נשאר ונצרך להיות התעוררות מחדש בכחן של בנ"י עצמם.

And because it was not by the merit of Yisrael, therefore it did not remain, and there needed to be a fresh awakening through the strength of Bnei Yisrael themselves.

A gift not earned does not endure; so a new arousal, generated by Bnei Yisrael's own avodah, is required to make the inspiration permanent.

ואני לדודי ואח"כ דודי לי וזה הוא דבר קיים לעד.

"I am for my Beloved," and afterward "my Beloved is for me" — and this is a thing that endures forever.

When the person initiates ("I am for my Beloved") and only then Hashem responds, the bond is self-earned and therefore everlasting.

וע"ז יש משפט בר"ה ויוכ"פ וזוכין בנ"י לתורה ע"י מעשיהם והוא שמחת תורה בשלימות:

And for this there is judgment on Rosh Hashanah and Yom Kippur, and Bnei Yisrael merit the Torah through their deeds, and this is the joy of the Torah in its completeness.

The judgment of the Yamim Nora'im is the process by which Bnei Yisrael earn the Torah through their own efforts, culminating in the full, lasting simchah of Simchas Torah.

Summary: Elul, whose name is hinted in "I am for my Beloved and my Beloved is for me," is the season when Bnei Yisrael initiate teshuvah and arouse an eis ratzon. Unlike the free Heavenly gifts of Pesach and Shavuos, which do not endure precisely because they were unearned, the bond awakened by a person's own avodah in Elul — refined through the judgment of Rosh Hashanah and Yom Kippur — is everlasting, reaching its complete joy on Simchas Torah.