This spring, the media mogul Stephen E. Strang made an unusual apology to readers in the pages of his glossy magazine. Mr. Strang presides over a multimillion-dollar Pentecostal publishing empire, Charisma Media, which includes a daily news site, podcasts, a mobile app and blockbuster books. At 70, he is a C.E.O., publisher and seasoned author in his own right. Despite all that, Mr. Strang worried something had gone awry.