Not every state (or county in every state) has a shall-issue policy; you can be denied for any reason. That's the way it is in my county in New York. But they probably do have to tell you, in writing, why you have been denied the permit.
Around here, outright lies or lies of omission on your application will result in an automatic rejection.
Obviously, a felony conviction, pending charges for a felony crime, having a restraining order against you, being involuntarily committed to a psychiatric institution, etc. is an automatic disqualification even to purchase a firearm.