Decaying mountain ranges often show a surprisingly dynamic pattern of landscape evolution. Although one might expect a simple, monotonic decline in relief over time, evidence from several inactive mountain ranges shows alternating sequences of deposition and erosion in the associated basins, suggesting variations in relief and exhumation rate in the ranges themselves. Examples include the Southern Rocky Mountains, the Pyrenees, the European Alps and the Atlas Mountains. In this paper, we explore the possible origins of post-orogenic landscape dynamics using a simple mathematical model of a mountain range and an adjacent foreland basin. The analysis highlights the importance of mass balance. In particular, a switch from basin exhumation to renewed sedimentation requires either an increase in sediment influx from the range or a decrease in sediment outflux beyond the basin margin. Although it is widely understood that post-orogenic changes in erosion and sediment flux can have multiple causes (including climate change, regional tectonic uplift or tilting, or exhumation of variable lithologies), an important implication of our analysis is that the impact of such changes must differ in sign or magnitude between the range and the basin to be recorded. This requirement places an important constraint on viable explanations for alternating sequences of deposition and erosion in a decaying mountain-basin pair.