Total proton reaction cross sections have been measured at 14.5 MeV for 22 separated isotope targets to an accuracy of ±2% for Ti, Fe, Ni, Cu, Zn, and Zr isotopes and ±4½% for the Sn isotopes. A beam-attenuation technique employing a solid-state counter to detect elastically scattered protons at forward angles has been used. Use of the solid-state detector reduces the corrections due to inelastic processes to a negligible level. The total reaction cross sections for the Fe, Ni, Zn, and Zr isotopes increase more rapidly with increasing N than optical-model calculations based on 14.5-MeV elastic-scattering and polarization data predict. The measured values for Fe, Ni, Cu, Zn, and Zr isotopes were generally smaller than the optical-model predictions; the measured Sn values, however, were larger. The dip in σR near Ni, previously observed using elemental targets in a number of experiments, is reproduced by suitable averaging of the isotope reaction cross sections. The dip is shown to arise from a combination of a sharply rising σR with increasing N (for constant Z) and the relatively small average value of N for Ni due to shell closure.