1) Bullheadedness 2) Impenitency 3) Irrepentance 4) Lack of contrition 5) Obstinacy 6) Obstinance 7) Pigheadedness 8) Recusance 9) Self-will 10) Stubbornness 1) Impenitency 2) Unrepentance 
• (n.) The condition of being impenitent; failure or refusal to repent; hardness of heart.
Im·pen'i·tence noun [ Latin impenitentia : confer French impénitence .] The condition of being impenitent; failure or refusal to repent; hardness of heart. « He will advance from one degree of wickedness and impenitence to another.» Rogers. 
[n] - the trait of refusing to repent
impenitency noun the trait of refusing to repent