Monsoon systems around the world are governed by the so-called moisture-advection feedback. Here we show that, in a minimal conceptual model, this feedback implies a critical threshold with respect to the atmospheric specific humidity q c o over the ocean adjacent to the monsoon region. If q c o falls short of this critical value q c oc, monsoon rainfall over land cannot be sustained. Such a case could occur if evaporation from the ocean was reduced, e.g. due to low sea surface temperatures. Within the restrictions of the conceptual model, we estimate q c oc from present-day reanalysis data for four major monsoon systems, and demonstrate how this concept can help understand abrupt variations in monsoon strength on orbital timescales as found in proxy records.