Appeals against failed applications for promotion have been referred to as the black hole of university-sector industrial relations. And there are reasons for that view.
Most often, either agreements or policies limit such appeals to grounds of procedural error (or bias) — rather than on the merits of an application. This limitation derives from a belief that it's inappropriate to second-guess necessarily subjective assessments. In other words, it's accepted that it's impossible to exactly and reproducibly quantify the relative merits of "knowledge worker" applications.
But even if we didn't accept the above presumptions, it's useful to predict the unwillingness of a judge, commissioner or other arbitrator to supplant his or her view (or logic) for that of a university-level, specialist, peer-review panel.
Assuming the constraint, even if there's been a demonstrable, procedural error, the appellant's troubles aren't done: There's a burden to show that any error was sufficiently serious to have affected the outcome.
And then, finally, if there has been procedural error and it has been of sufficient gravity to have potentially affected the outcome: What's the remedy?
A likely decision is to refer the matter back to the original panel to reconsider the decision absent the element that gave rise to error.
Of course they're happy to see the application again.
Reputation is an idle and most false imposition;
oft got without merit, and lost without deserving.
—William Shakespeare (1564-1616)