We measured the energy dependence of the total reaction cross sections ( σR ) for the proton drip-line nucleus of neon isotopes, 17 Ne, with a solid hydrogen target. The σR on a proton target in the low- and intermediate-energy regions were provided, where only a few values are available for unstable nuclei. The new data were compared with theoretical calculations using the Glauber model. In the low-energy region (∼100 A MeV), the theoretical cross sections overestimate the experimental ones, whereas the theoretical ones significantly underestimate the experimental data in the intermediate energy region (∼300-500 A MeV). We discuss several possibilities for solving this discrepancy. This work suggests the necessity of more careful investigations of the energy dependence of σR for various nuclei on a proton target to determine the nuclear size properties precisely.