Our appeal was denied on the grounds thst one more would prejudice efficient education if they exceeded their PAN. Odd, since my son had forced the school's rep. to say 3 times that one more would not prejudice anything!
Sorry to hear your news.
If you were the only appeal, then this does sound very odd. If, however, there were other people appealing, then they might have had stronger grounds than you.
As an example, say that a LEA grammar school has a PAN of 87, so the LEA only allocate 87 places. The classes are arranged with 30 seats and each previous year has had around 90 pupils after appeals, and the statement from the head says they can take 90 without problems. At the appeal, the panel might ask the presenting officer (if the parents haven't picked it up first) every time why there is the difference, and thus established that should they be thus minded and the cases are strong enough, they can allow 3 appeals (or more in truly exceptional circumstances).
Now If there's 15 parents appealling, even though they all ask the question, only the three with the strongest reasons will be allowed.
If there's only 2 appealing, yet they're both non-qualifiers, then they would also have to have very strong reasons why they didn't pass.