Contradiction with Psalms 44:9
While Psalms 20:6 expresses confidence in God's saving power, Psalms 44:9 describes a situation where God has seemingly rejected and not gone forth with armies.
Psalms 44:9: But thou hast cast off, and put us to shame; and goest not forth with our armies.
Contradiction with Psalms 88:14
Psalms 20:6 is about assurance of God's help, but Psalms 88:14 questions why God casts off the soul and hides His face.
Psalms 88:14: LORD, why castest thou off my soul? [why] hidest thou thy face from me?
Contradiction with Habakkuk 1:2
In contrast to the certainty of salvation in Psalms 20:6, Habakkuk 1:2 reflects a cry for help and a feeling of not being heard by God.
Habakkuk 1:2: O LORD, how long shall I cry, and thou wilt not hear! [even] cry out unto thee [of] violence, and thou wilt not save!
Contradiction with Job 30:20
This verse contradicts the assurance in Psalms 20:6 by depicting Job calling for help but not receiving an answer.
Job 30:20: I cry unto thee, and thou dost not hear me: I stand up, and thou regardest me [not].