A new direct measurement of the ${}^{59}Cu(p,\alpha ){}^{56}Ni$ excitation function from 2.43–5.88 MeV in the center-of-mass was performed in inverse kinematics using the high-efficiency MUSIC active-target detector at FRIB. This reaction plays a critical role in constraining the strength of the NiCu cycle in different explosive astrophysical scenarios such as Type I X-ray bursts and the $\nu$p-process in neutrino-driven winds after a core-collapse supernova. The newly derived stellar rate is systematically lower than previous estimates, reducing NiCu-cycle recycling in X-ray bursts to below $0.74\%$ and enhancing the $\nu p$-process efficiency across the relevant temperature range, extending its operation up to $T_9={3.94}_{-0.85}^{+0.99}$ while constraining the predicted endpoint.