We present multiwavelength follow-up observations of the ATLAS discovered faint Iax supernova SN 2020kyg that peaked at an absolute magnitude of M-g approximate to -14.9 +/- 0.2, making it another member of the faint Iax supernova population. The bolometric light curve requires only approximate to 7 x 10(-3) M-circle dot of radioactive Ni-56, with an ejected mass of M-ej similar to 0.4 M-circle dot and a low kinetic energy of E approximate to 0.05 +/- 0.02 x 10(51) erg. We construct a homogeneous volume-limited sample of 902 transients observed by ATLAS within 100 Mpc during a 3.5 yr span. Using this sample, we constrain the rates of faint Iax (M-r greater than or similar to -16) events within 60 Mpc at 12(-8)(+1)(4) per cent of the SN Ia rate. The overall Iax rate, at 15(-9)(+)(17) per cent of the Ia rate, is dominated by the low-luminosity events, with luminous SNe Iax (M-r less than or similar to -17.5) like 2002cx and 2005hk, accounting for only 0.9(-0.5)(+1.1) per cent of the Ia rate (a 2 sigma upper limit of approximately 3 per cent). We favour the hybrid CONe WD + He star progenitor channel involving a failed deflagration of a near Chandrasekhar mass white dwarf, expected to leave a bound remnant and a surviving secondary companion, as a candidate explanation for faint Iax explosions. This scenario requires short delay times, consistent with the observed environments of SNe Iax. Furthermore, binary population synthesis calculations have suggested rates of 1-18 per cent of the SN Ia rate for this channel, consistent with our rate estimates.