It'll mutate the replicators and throw a new beast at the problem. If that doesn't work it'll try again with another beast, and another, and another. Here's the secret. Not all mutation cause a change in the phenotype of the replicator.
Mutations occur and the beast remains at the same spot on the fitness landscape.
This combination creates a big jump that no single mutation can do by itself. Evolution can continue this process ad infinitum until it finally gets out. Evolution never gets stuck. Also, in the real world, the fitness landscape is not static.