Today I heard part of a shiur from Dr. Leiman on the source of saying Li'dovid Hashem in Elul.
I saw a reason offered by the Rosh Yeshiva of Chevron Rav Yechezkal Sarna in his Dlayos Yechezkel: Elul is SCARY [see above post]. The theme of Li'dovid Hashem is HOPE.
Scary - but קוה אל ה' חזק ויאמץ לבך