Solids flow through an orifice at the bottom of a standpipe, against a counterflow of gas, becomes unstable as the gas flow is increased. In the unstable condition, the solids flow in the standpipe is jerky, reflecting the oscillations between flow and no flow at the orifice, and resembles slip-stick flow. Practical operation of these systems requires a straightforward quantitative demarcation for distinguishing when flow behaviour changes from stable to unstable. This paper presents an analysis of flow stability in standpipes with gas counterflow, supported by small-scale experiments. For smaller orifices, solids flow instability occurs when a hemispherical bubble cap just spans the orifice, corresponding to a certain critical negative pressure gradient. For large orifices, stable solids flow is abruptly cut off when the counterflowing gas rate is high enough, and no unstable solids flow region occurs.