We report a comprehensive de Haas-van Alphen (dHvA) study of the heavy-fermion material CeRhIn_{5} in magnetic fields up to 70 T. Several dHvA frequencies gradually emerge at high fields as a result of magnetic breakdown. Among them is the thermodynamically important β_{1} branch, which has not been observed so far. Comparison of our angle-dependent dHvA spectra with those of the non-4f compound LaRhIn_{5} and with band-structure calculations evidences that the Ce 4f electrons in CeRhIn_{5} remain localized over the whole field range. This rules out any significant Fermi-surface reconstruction, either at the suggested nematic phase transition at B^{*}≈30 T or at the putative quantum critical point at B_{c}≃50 T. Our results rather demonstrate the robustness of the Fermi surface and the localized nature of the 4f electrons inside and outside of the antiferromagnetic phase.