Why doesn't Satan repent?

Satan cannot repent because the Lord has not granted him repentance. Only when the Lord grants repentance will it happen, as Paul teaches:

Acts 5:31 “He is the one whom God exalted to His right hand as a Prince and a Savior, to grant repentance to Israel, and forgiveness of sins. 

Acts 11:18 When they heard this, they quieted down and glorified God, saying, “Well then, God has granted to the Gentiles also the repentance that leads to life.” 

2Cor. 7:9 I now rejoice, not that you were made sorrowful, but that you were made sorrowful to the point of repentance; for you were made sorrowful according to the will of God, so that you might not suffer loss in anything through us. 
2Cor. 7:10 For the sorrow that is according to the will of God produces a repentance without regret, leading to salvation, but the sorrow of the world produces death. 

2Tim. 2:25 with gentleness correcting those who are in opposition, if perhaps God may grant them repentance leading to the knowledge of the truth, 

The repentance that leads to salvation and a changed heart is a work done by God alone in the heart of a person, so unless God grants repentance, a person (or angel) cannot repent of sin. 
Furthermore, the Bible says it is not in God’s plan to grant mercy to fallen angels like Satan:

Heb. 2:16 For assuredly He does not give help to angels, but He gives help to the descendant of Abraham. 

Therefore, God has no plans to grant repentance to Satan, so therefore he will not ever repent.