ABSTRACT We present multiwavelength follow-up observations of the ATLAS discovered faint Iax supernova SN 2020kyg that peaked at an absolute magnitude of Mg ≈ −14.9 ± 0.2, making it another member of the faint Iax supernova population. The bolometric light curve requires only ≈7 × 10−3 M⊙ of radioactive 56Ni, with an ejected mass of Mej ∼ 0.4 M⊙ and a low kinetic energy of E ≈ 0.05 ± 0.02 × 1051 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 (Mr ≳ −16) events within 60 Mpc at $12^{+14}_{-8}{{\ \rm per\ cent}}$ of the SN Ia rate. The overall Iax rate, at $15^{+17}_{-9}{{\ \rm per\ cent}}$ of the Ia rate, is dominated by the low-luminosity events, with luminous SNe Iax (Mr ≲ −17.5) like 2002cx and 2005hk, accounting for only $0.9^{+1.1}_{-0.5}{{\ \rm per\ cent}}$ of the Ia rate (a 2σ 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 $1\!-\!18{{\ \rm per\ cent}}$ of the SN Ia rate for this channel, consistent with our rate estimates.