We have performed resistivity and inelastic neutron scattering measurements on three samples of Fe0.98-zCuzTe0.5Se 0.5 with z=0, 0.02, and 0.1. It is found that with increasing Cu doping the sample's resistivity deviates progressively from that of a metal. However, in contrast to expectations that replacing Fe with Cu would suppress the magnetic correlations, the low-energy (≤12 meV) magnetic scattering is enhanced in strength, with greater spectral weight and longer dynamical spin-spin correlation lengths. Such enhancements can be a consequence of either enlarged local moments or a slowing down of the spin fluctuations. In either case, the localization of the conduction states induced by the Cu doping should play a critical role. Our results are not applicable to models that treat 3d transition metal dopants simply as effective electron donors. © 2013 American Physical Society.