Cyclonic low-pressure systems (LPS) produce abundant rainfall in South Asia, where they are traditionally categorized as monsoon lows, monsoon depressions, and more intense cyclonic storms. The India Meteorological Department (IMD) has tracked monsoon depressions for over a century, finding a large decline in their number in recent decades, but their methods have changed over time and do not include monsoon lows. This study presents a fast, objective algorithm for identifying monsoon LPS in high-resolution datasets. Variables and thresholds used in the algorithm are selected to best match a subjectively analyzed LPS dataset while minimizing disagreement between four atmospheric reanalyses in a training period. The streamfunction of the 850 hPa horizontal wind is found to be the best variable for tracking LPS; it is less noisy than vorticity and represents the complete non-divergent wind, even when flow is not geostrophic. Using this algorithm, LPS statistics are computed for five reanalyses, and none show a detectable trend in monsoon depression counts since 1979. Both the Japanese 55-year Reanalysis (JRA-55) and the IMD dataset show a step-like reduction in depression counts when they began using geostationary satellite data, in 1979 and 1982 respectively; the 1958-2018 linear trend in JRA-55, however, is smaller than in the IMD dataset and its error bar includes zero. There are more LPS in seasons with above-average monsoon rainfall and also in La Nina years, but few other large-scale modes of interannual climate variability are found to modulate LPS counts, lifetimes, or track length consistently across all reanalyses.