Despite their different implementations, comparison of the best threading approaches to the prediction of evolutionary distant protein structures reveals that they tend to succeed or fail on the same protein targets. This is true despite the fact that the structural template library has good templates for all cases. Thus, a key question is why are certain protein structures threadable while others are not. Comparison with threading results on a set of artificial sequences selected for stability further argues that the failure of threading is due to the nature of the protein structures themselves. Using a new contact map based alignment algorithm, we demonstrate that certain folds are highly degenerate in that they similar can have very coarse grained fractions of native contacts aligned and yet differ significantly from the native structure. For threadable proteins, this is not the case. Thus, contemporary threading approaches appear to have reached a plateau, and new approaches to structure prediction are required.