What is the best way to craft the appeal letter based on health issues to have one last chance for taking the qualifying exam? Those health and mental issues have been already documented through a medical doctor and a licensed psychological counselor. Please, anybody has such advices or suggestions to draft the letter in a way that showing how the health issues have a significant impacts on qualifying exam preparation.
If this is in the US, the precise nature of your health issues is protected by HIPAA and is none of your department's business. Documentation affirming only that those health issues have substantially interfered with your academic performance should be issued by your disability services office, who have experience with such things. Medical disabilities are disabilities and as such are legally entitled to reasonable accommodation.