Direct measurements of the gain profile of optically pumped far-infrared lasers show that large shifts in the laser frequency can be caused by the absorption from thermal molecules on the laser transition. The absorption shifting greatly exacerbates pump frequency deviations, resulting in an extreme sensitivity to pump offsets and drifts. This pressure-dependent shifting mechanism is not present in transversely pumped lasers, which explains their superior frequency reproductibility compared to longitudinally pumped lasers, and reconciles two apparently conflicting results regarding laser stability.