Can the sins of someone who committed adultery intentionally and repeatedly, despite knowing its prohibition, be forgiven if he then repents sincerely and regrets his actions, and vows to Allah not to return to the sin, or does the intentional repetition of the sin prevent forgiveness?

The door of repentance is open until the sun rises from its west. If you offer sincere repentance that fulfills its conditions—namely, abstaining from sins, resolving not to return to them, and regretting having committed them—then Allah will accept your repentance and forgive you. For Allah Almighty's forgiveness is greater than any sin, as confirmed by His saying: "And it is He who accepts repentance from His servants and pardons sins" and "Say, 'O My servants who have transgressed against themselves [by committing sins], do not despair of the mercy of Allah. Indeed, Allah forgives all sins.'" And the Prophet, peace be upon him, said: "The one who repents from sin is like one who has no sin." Therefore, have a good opinion of Allah, increase in acts of obedience and supererogatory acts of worship, for good deeds erase bad deeds. And distance yourself from the causes of disobedience, associate with the righteous, safeguard your obligatory prayers, increase in supererogatory acts, and adhere to remembrance of Allah, supplication, and seeking forgiveness.