Most quantum point contacts (QPCs) fabricated in high-mobility 2D electron gases show a zerobias conductance peak near pinchoff, but the origin of this peak remains a mystery. Previous experiments have primarily focused on the zero-bias peak at moderate conductance, in the range 1 − 2e 2 /h. Here, measurements are presented of zero-bias peaks that persist down to 10 −4 e 2 /h. Magnetic field and temperature dependencies of the zero-bias peak in the low-conductance limit are qualitatively different from the analogous phenomenology at higher conductance, with implications for existing theoretical models of transport in low-density QPCs.