Hi i might not be able to help much but ill try.My twins took the kent test,one passed and one failed quite badly.
our headteacher did not appeal for her because the scores were what she considered to be low but she did write a supporting letter as did her actual teacher stating my daughter is a good candidate for grammar school and this is mainly based on her academic ability.
academic ability is the most important thing along with the fact that you must provide a mitigating circumstance as to why your child under achieved in the test if they are indeed of high ability.
our head teacher has also told us that even for pupils who were only a few points out her appeals were not sucsessful and that parent appeals are more often sucsessful than those from head teachers-she has told us this lots of times throughout the process.
do you have predictions? my daughter is a level 5,you need to really be predicted to have a child at level 5 in maths,english and science and obviously 5a is better than b or c but any 5 is good and you need that really.
you should mention anything you feel is relevant to an under achievement on the day,i cannot prove my daughters mitigating circumstances.to do that i woould have had to stopped her from entering the test anyway taken her to a doctor and asked him to examine her in a way that i am positively sure he would refuse to do as it was not an actual medical neccesity.
But of course you do need to include all of the evidence you can provide.
you have nothing to lose,like me your child has unfortunately failed the test and although the chances of sucsess are slim if you dont try you have no chance.my daughter really wants to try so i agreed,ive told her she has a very remote chance so shes prepared but its not impossible and i think where theres the smallest of chances if you and your family want to appeal you should.
now i have waffled on but thats me for you
good luck,i posted our letters today (appealing to both first and second choices) and i know that it could take until june to get an answer and i feel sick with nerves already.