Using a complete sample of ~300 star-forming galaxies within 11 Mpc of the Milky Way, we evaluate the consistency between star formation rates (SFRs) inferred from the far ultraviolet (FUV) non-ionizing continuum and Hα nebular emission, assuming standard conversion recipes in which the SFR scales linearly with luminosity at a given wavelength. Our analysis probes SFRs over 5 orders of magnitude, down to ultra-low activities on the order of ~10-4 M sun yr-1. The data are drawn from the 11 Mpc Hα and Ultraviolet Galaxy Survey (11HUGS), which has obtained Hα fluxes from ground-based narrowband imaging, and UV fluxes from imaging with GALEX. For normal spiral galaxies (SFR ~ 1 M sun yr-1), our results are consistent with previous work which has shown that FUV SFRs tend to be lower than Hα SFRs before accounting for internal dust attenuation, but that there is relative consistency between the two tracers after proper corrections are applied. However, a puzzle is encountered at the faint end of the luminosity function. As lower luminosity dwarf galaxies, roughly less active than the Small Magellanic Cloud, are examined, Hα tends to increasingly underpredict the total SFR relative to the FUV. The trend is evident prior to corrections for dust attenuation, which affects the FUV more than the nebular Hα emission, so this general conclusion is robust to the effects of dust. Although past studies have suggested similar trends, this is the first time this effect is probed with a statistical sample for galaxies with SFR lsim 0.1 M sun yr-1. By SFR ~ 0.003 M sun yr-1, the average Hα-to-FUV flux ratio is lower than expected by a factor of two, and at the lowest SFRs probed, the ratio exhibits an order of magnitude discrepancy for the handful of galaxies that remain in the sample. A range of standard explanations does not appear to be able to fully account for the magnitude of the systematic. Some recent work has argued for a stellar initial mass function which is deficient in high-mass stars in dwarf and low surface brightness galaxies, and we also consider this scenario. Under the assumption that the FUV traces the SFR in dwarf galaxies more robustly, the prescription relating Hα luminosity to SFR is re-calibrated for use in the low SFR regime when FUV data are not available.