I wonder how many pupils The Crypt actually take per year. They say in their appeal's letter that their net capacity is 112. As it stands they have already allocated 108 places leaving a mere 4 for appeals!! (panic rising!) I thought that they took 120? Which would be a little better.
They are not allowed to hold back places for appeals. They must allocate all those who passed to fill whatever their IAN/PAN is. They're not allowed to fill empty places from those who didn't pass as they're a selective school.
By the figures you give, 4 less boys passed than they had spaces for. The Appeals Panel may (but don't have to) allow 4 appeals before having to consider prejudice against the existing pupils.
However, if you (or other parents) can prove that they've coped with more than 112 in the past, then the panel may allow more appeals than 4. But that does rather depend on if they think the boys should have passed the exam if they didn't have mitigating circumstances.
The Elephant in the Room is that the school probably want the panel to allow the appeals, to keep numbers/finances up, but are not allowed to say so, either in private to the panel (and the school side should never be in contact with the panel when the parents are not there) or in public (during appeals). The best they can do is put up a very weak defence.
So don't panic.