It will take time to create a new reputation and some people do have the flexibility of mind to say "Oh he's doing better and I am going to take it on faith that that will continue, and if he does relapse we will cross that bridge if and when we come to it".. Other people carry around the pain of betrayal and now refuse to trust anyone who claims to have changed.. maybe they themselves have struggled to change something and have not been able to and so they assume people can't change.. or they've been consistently disappointed by someone, maybe the absent father or husband who has said a million times that he will start being better and never follows through.. There's a mentality that if you trust, you WILL get hurt, and that once an alcoholic/cheat/liar, always that.. We know it's not true but we have to be sympathetic to those who have been conditioned to never put their trust back in to a person who has done wrong. And set realistic expectations - a large part of the world around us is of that "trust no one" mentality.