In this paper, we measure the far-infrared (FIR) and radio flux densities of a sample of 82 local gas-rich galaxies, including 70 'dwarf' galaxies (M* < 109M⊙), from the Local Volume HI Survey (LVHIS), which is close to volume limited. It is found that LVHIS galaxies hold a tight linear FIR-radio correlation (FRC) over four orders of magnitude (F1.4GHz ∝ F1.00±0.08 FIR ). However, for detected galaxies only, a trend of larger FIR-to-radio ratio with decreasing flux density is observed. We estimate the star formation rate by combining UV and mid- IR data using empirical calibration. It is confirmed that both FIR and radio emission are strongly connected with star formation but with significant non-linearity. Dwarf galaxies are found radiation deficient in both bands, when normalized by star formation rate. It urges a 'conspiracy' to keep the FIR-to-radio ratio generally constant. By using partial correlation coefficient in Pearson definition, we identify the key galaxy properties associated with the FIR and radio deficiency. Some major factors, such as stellar mass surface density, will cancel out when taking the ratio between FIR and radio fluxes. The remaining factors, such as HI-tostellar mass ratio and galaxy size, are expected to cancel each other due to the distribution of galaxies in the parameter space. Such cancellation is probably responsible for the 'conspiracy' to keep the FRC alive.