What is the ruling on one who repents but is unable to erase the traces of his ongoing sins?

Whoever repents to Allah with a sincere repentance by abandoning the sin, regretting having committed it, and resolving not to return to it, has fulfilled what Allah has made obligatory upon him. Allah Almighty will forgive him what has passed through His mercy, for sincere repentance erases what came before it, and one who repents from a sin is like one who has no sin. Nor is he harmed by the continued presence of those who commit that sin after him.