After adultery many times, one feels hopeless and there is no saving the soul.

Never despair from the mercy of Allah. Allah says that if your sins were to be written in books and the books were to reach the skies and you turned to him and asked him for forgiveness, he would forgive you. He is the most merciful. Never despair. It's a trick from shaitan. Just turn your hands and raise them to Allah subhanahu wa ta'ala. Make dua and Allah will do the rest.