We discuss the nonlocality of W and Dicke states subject to losses. We consider two noise models, namely, loss of excitations and loss of particles, and investigate how much loss can be tolerated such that the final state remains nonlocal. This leads to a measure of robustness of the nonlocality of Dicke states, with a clear physical interpretation. Our results suggest that the relation between nonlocality and entanglement of Dicke states is not monotonic.