Surrender is not a term used in the New Testament. It is used in church circles usually referring to the biblical concept of submission or yielding. Using the word surrender, I believe, has a subtle impact on how we view God. The term surrender makes it out as though we are at war with God and we give up when He beats us down enough. But God is loving and in no way punishes His children (see 1 John 4:18). Scripture never uses the language of surrender of us in relation to God.
In some contexts the Greek word for "submit" is translated as "be subject" and may have the idea of being subordinate to God in a military fashion. Even there the idea of surrender does not fit because we are on God's side. He is for us, He is never against us. We are not at war with Him and we are not to surrender to Him as if we were.
Prominent Definitions of the English Word "Surrender"
acceptance of despair; the act of admitting defeat; to relinquish to the control or possession under threat, compulsion, or demand; to give (oneself) up, as or as if to an enemy
"Submit to God" -James 4:7
The Greek word translated "submit" in James 4:7 refers to "a voluntary attitude of cooperation." Cooperation is "working or acting together; agreeing." Biblical submission is a loving trust. It does not have the attitude of "because I have to.." or "since you're forcing me too.." Biblical submission says "I trust your desires are good and loving. I love you so I agree to work with you to fulfill your desires." This is how we are to obey God. Obedience is not merely an outward action in accordance with an instruction. Obedience is an inward trust based on God's love and guidance that results in outward action. There is nothing in the Christian life that does not involve God's love for you and your trust of Him.
The Christian does not need to "surrender daily" but to cooperate with what the Spirit of God communicates over the course of each day. Submission is a situational decision not a blanket declaration. You cannot submit your day to God. You can only submit as life rolls on throughout the day, anything else is pretending. Submission is relational cooperation done in the present tense. Submission is not tapping out because God twists your arm, it is tapping in, into the life, love, and relationship that God has given you with Himself. You cannot give your life to God. As a Christian God gave His life to you. He is your life (see Colossians 3:3-4). We are to simply walk with Jesus in newness of the new life He has given us. There is no promise to make or achievement to grasp just trust God and His love for you as in live in Him and with Him.
See Also: Why I Will Never Surrender to God