I am sorry to hear about your disappointing results.
I am going to partially disagree with Capers on this. In the Head's manual for the 11+ process, Bucks make the following statement regarding sick children:
As the dates of the tests are published in advance to parents it should be assumed that any child in school on the day of a test is well enough to take part. Please discourage children who are evidently not well from taking the test.
Parents often offer a child being ill on the day of a test in mitigation for their under performance and it can be avoided in many cases by parents and teachers recognising that a child is unwell and withdrawing them from the test on that occasion.
Unfortunately they do not make the same statement in the Admissions brochure provided to parents, so unless the Head was proactive in talking to you about wther your son was fit to take the test (and there are huge numbers of Heads who don't seem to even Read The Flippin' Manual) you were not to know that.
The only statement in the Admissions brochure is:
"Children can be tested later ..., for example if they are ill on the day of the test."
Appeal panels really do not like "sick kiddy stories", and they take the view that, if a child is well enough to be in school, they are well enough to take the test. I recommend that you play it down, and make it a "brief mention": "Although he seemed to have recovered fully by the day of the test, perhaps, in hindsight, that wasn't quite the case."
Concentrate instead on finding the strongest possible academic evidence that you can.
You will find more advice in the 11+ Appeals Q&A - the link is at the top of the page.