To whom does he say "Kave El Hashem"?
Radak: Amidst my great trust and Emunah in Hashem, I say so to myself the entire day. Do not be concerned for the enemies' words!
Malbim: David commands so. Hope in Hashem is unlike hope in people in two ways. (a) Hope in another is a deferred hope that makes the heart ill. Hope in Hashem strengthens the heart - "Chazak v'Ya'ametz Libecha"! (b) Refer to 27:14:3:3.
Why did he say "Chazak v'Ya'ametz Libecha"?
Radak: If you persist in His ways, He will strengthen your heart not to be weakened via the enemies, and you will find strength in your heart.
Why is "Kave El Hashem" repeated?
Rashi (from Brachos 32b): If Your prayer is not accepted, hope (pray) again!
Radak: You should always have hope in Him. It should not depart from your heart.
Malbim: Hope in another is not an end unto itself; the purpose is the requested matter. He hopes that he will not need to hope more! Hope in Hashem itself is itself desired, to strengthen his heart and hope again.
