Plasmonic modes with long radiative lifetimes, subradiant modes, combine strong confinement of the electromagnetic energy at the nanoscale with a steep spectral dispersion, which makes them promising for biochemical sensors or immunoassays. Subradiant modes have three decay channels: Ohmic losses, their extrinsic coupling to radiation, and possibly their intrinsic dipole moment. In this work, the performance of subradiant modes for refractive index sensing is studied with a general analytical and numerical approach. We introduce a model for the impact that has different decay channels of subradiant modes on the spectral resolution and contrast. It is shown analytically and verified numerically that there exists an optimal value of the mode coupling for which the spectral dispersion of the resonance line shape is maximal The intrinsic width of subradiant modes determines the value of the dispersion maximum and depends on the penetration of the electric field in the metallic nanostructure. A figure of merit given by the ratio of the sensitivity to the intrinsic width, which are both intrinsic properties of subradiant modes, is introduced. This figure of merit can be directly calculated from the line shape in the far field optical spectrum and accounts for the fact that both the spectral resolution and contrast determine the limit of detection. An expression for the intrinsic width of a plasmonic mode is derived and calculated from the line shape parameters and using perturbation theory. The method of analysis introduced in this work is illustrated for dolmen and heptamer nanostructures. Fano-resonant systems have the potential to act as very efficient refractive index sensing platforms compared to Lorentz-resonant systems due to control of their radiative losses. This study paves the way toward sensitive nanoscale biochemical sensors and immunoassays with a low limit of detection and in general, any nano-optical device where Ohmic, losses limit the performance.