The five performers, laid off last month, asked the High Court for an injunction so they could keep their jobs pending a legal challenge.
Judge Ross Cranston refused Tuesday, saying reinstating the musicians would cause "not insignificant practical difficulty" for the company. But he said the five had a strong case to argue for breach of contract.
The story of a horse serving during World War I is one of the National Theatre's most successful shows, with productions running in Britain, the United States and Germany. Steven Spielberg directed a film adaptation.
The theater says none of the other productions features live musicians.