More questions than answers:
Does this question pertain to you or your child?
Is there adequate documentation of the illness? doctor’s note, formal diagnosis etc?
Is the HS guidance counselor aware of the issue so he/she can write a letter on your behalf?
Will the health issues be fully resolved by the fall?
Is there a chance to retake any dropped classes over the summer if necessary?
As I said in the first post, I would suggest that the student contact Harvard admissions to go over his/her particular situation. Get any answer in writing.