The court of appeals cannot simply refuse to hear the appeal.
The Trump campaign has the right to an appeal to the U.S. Court of Appeals. Once there, the court has some discretion as to how quickly it hears the case, how much time it spends on the case, and how much detail it offers in explaining its final decision. But it may not simply choose not to hear the case.
The campaign is not, however, permitted to file an appeal if there is no good-faith basis for it, nor may it file an appeal merely to delay the outcome it seeks to avoid, and the district court's findings seem to be designed to flag this as a potential issue for the circuit court. If that court thinks the appeal is frivolous, it would likely issue a show-cause order requiring the campaign to explain why the appeal should not be dismissed.
In any event, the court cannot simply assess the case as weak and dismiss it without giving the campaign a chance to explain why that is the wrong choice.
If Trump is unsuccessful before a panel of the Court of Appeals for the Third Circuit, he may ask the entire Third Circuit to hear the case, and he may seek review at the Supreme Court. Neither court is required to hear the case at all, or to explain why it chose not to. In the vast majority of cases, the court simply refuses to hear cases with a one-sentence order. Given the nature of the case, though, it is reasonably likely that at least one member of the court would write to discuss the court's decision.