Your boyfriend is really lucky to have you in his life, and I am sure he appreciates your compassion. You should definitely take the advice of the people who have responded already - keep eye contact, acknowledge when a phrase gets out but it was really difficult for him, respond to the content of what he is saying not how he said it, and stick up for him in social situations. When you are direct and honest, his anxiety will decrease and therefore help him be more fluent.