In a previous paper, we have demonstrated that a microcrystalline copper film well bonded to a polymer substrate can be stretched beyond 50% without cracking. The film eventually fails through the coevolution of necking and debonding from the substrate. Here we report much lower strains to failure (approximately 10%) for polymer-supported nanocrystalline metal films, the microstructure of which is revealed to be unstable under mechanical loading. We find that strain localization and deformation-associated grain growth facilitate each other, resulting in an unstable deformation process. Film/substrate delamination can be found wherever strain localization occurs. Therefore, we propose that three concomitant mechanisms are responsible for the failure of a plastically deformable but microstructurally unstable thin metal film: strain localization at large grains, deformation-induced grain growth, and film debonding from the substrate.