The Huygens probe landed in a damp lake bed fed by fluvial channels, indicative of past rainfall. Such washes, interspersed with vast dunes, are typical of Titan's tropical landscape. Yet, Cassini-Huygens measurements reveal a highly stable tropical atmosphere devoid of deep convective storms, and the formation of washes in dune fields is not understood. Here we examine the effects of seasonal variations in humidity, surface heating, and dynamical forcing on the stability of Titan's troposphere. We find that during the probe landing, the middle troposphere was weakly unstable to convection, consistent with the tenuous cloud detected at 21 km. Yet the tropical atmosphere, at any season, is too stable to produce deep convective storms. Convection in the tropics remains weak and confined to altitudes below ∼30 km, unless the humidity is increased below 9 km altitude. Solar heating is insufficient to significantly humidify the tropical atmosphere. The large polar lakes are seasonably stable, and the methane column abundance measured by Huygens typical of the tropical atmosphere. Our study indicates the presence of distinct polar and equatorial climates. It also suggests that fluvial features in the tropics do not result from recent seasonal rainstorms, and thereby supports other origins such as geological seepage, cryovolcanism, or a wetter climate in the past.