The appeal can be dismissed if you do not follow the rather strict rules that govern appeals or if the appellate court concludes that the appeal is essentially frivolous.
An appeal also can be dismissed if the case becomes "moot". If the court can no longer give the requested relief the higher court will dismiss the appeal. For example, assume you have filed the appeal of an injunction prohibiting a strike. If the strike is settled before the appeal is heard, the higher court would dismiss the appeal as being "moot".