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Since the South Asia Summer Monsoon is the main source of water for a densely cultivated and climate-sensitive region, its predictability has long been the target of research. This work estimates the predictability horizon of monsoon precipitation amount by systematically comparing statistical forecasts made using information from different lead times before the monsoon start. Linear and nonlinear prediction methods are considered that use the leading modes of the global sea surface temperature field to forecast monsoon-season (June-September) total precipitation on a 0.5 degrees grid over South Asia, where each method is trained on data from 1901 to 1996 and evaluated on data from 1997 to 2017. Forecasts were found to outperform a climatology baseline up to at least 1 year ahead, with a nonlinear method (random forest) on average outperforming linear regression with group lasso, although with greater variability in skill across locations and years. Forecast performance measures (fractional reduction in root mean square error and information skill score) decreased with increasing lead time following exponential decay timescales of 5-12 months, depending on the performance measure and forecast method. Even at lead times of several years, there was some forecast skill compared to climatology, as a result of the impact of long-term climate change on monsoon precipitation. The results suggest that monsoon prediction is possible with longer lead times than generally attempted now.