If you fail a class you may receive what is called a "punitive grade" for that class. This means that the grade you receive earns credit towards your degree, even though it may bring your GPA down. Since this grade counts towards your degree requirements (even negatively) you are entitled to GI Bill benefits for any class you receive such a grade in.
A "non-punitive grade" is a grade that doesn't earn credit towards your degree. An example of this may be withdrawal after the drop period; or other things like auditing a class, academic probation, or suspension. Since non-punitive grades don't count towards your degree you may be required to repay any GI Bill money you received for such classes.