Leaving aside the particular circumstances of Katie's appeal (for which I have a great deal of sympathy and concern), appeal panels have very difficult judgments to make.
a child who otherwise performs well
Assessing the academic evidence is not entirely straightforward.
KS2 SATs predictions? - SATs are not comparable with the 11+.
Other standardised tests such as CATs? - They are standardised differently, and carried out under less stressful conditions.
Headteacher recommendation? - Panels know that headteachers often tend to be over-optimistic.
In my view IAPs should take account of the totality
of the academic evidence, and look to see whether all (or most) of the "indicators" are present. See Q&As, B11.
And assessing the extent to which a child was affected by particular circumstances is hardly an exact science either. If the pet rabbit died the night before the 11+, might it explain a shortfall of 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 marks? And what adjustment should be made if it had died 2 days before the 11+? Or a week? Or ten days? Or two weeks? Or three weeks?
I think most panels would sympathise with Worried Mum's traumatic circumstances as described above, especially if she submits evidence with the date of her father's hospitalisation, but even she acknowledges: "I don't know whether it [the result] is due to the stress of the family, or he would still have got that score."
I agree with Alex - I think the key to her appeal is whether there is strong alternative academic evidence to indicate that under normal circumstances her son would have qualified.