We have to distinguish between 'process' and 'judgement'.
You cannot challenge the panel's judgement - you can only look to see if there was any fault with the process.
Because there is evidence that your illness was
noted by the panel, the process was followed correctly.
Understandably you feel they should have given more weight to your illness, but that's a matter of judgement, and I'm afraid it's not something you can query.
However, I think it would be worth arguing that the clerk's notes are inadequate, and that it is unclear what criteria were being used in order to arrive at the decision about academic suitability.
You ought to try an appeal and see what happens.
If you haven't already seen it, section D of the following thread from last year will give you an idea of what lies ahead if you wish to appeal.viewtopic.php?f=12&t=36418