Does Allah forgive a sin that was repeated after repentance and a promise not to return to it? And is one punished who breaks his promise to Allah, especially if the sin is plucking eyebrows, which has been ruled as accursed?

Plucking the eyebrows is forbidden (haram). Allah the Almighty forgives His servant and accepts his repentance as long as he sins, seeks forgiveness, and fulfills the conditions of repentance. If a servant repents every time he sins, then Allah will accept his repentance, even if it happens repeatedly. As Allah the Almighty says: "Your Lord has decreed upon Himself mercy: that any of you who does wrong out of ignorance and then repents after that and corrects himself - indeed, He is Forgiving and Merciful." (Quran 6:54) And: "And whoever does a wrong or wrongs himself but then seeks forgiveness of Allah will find Allah Forgiving and Merciful." (Quran 4:110). Allah loves those who repent frequently, who repent from a sin even if it recurs from them. It is stated in a hadith: "A servant committed a sin... and his Lord said: 'My servant knew that he has a Lord who forgives sins and holds accountable for them; I have forgiven My servant.'" Even if this happens a hundred or a thousand times, Allah will accept his repentance. However, this is not a license to commit sins. The benefit of the hadith is that returning to repentance after repeated sinning is better than initiating it.