Understanding the Amazon Rainforest's response to shifts in precipitation is paramount with regard to its sensitivity to climate change and deforestation. Studies using Dynamic Global Vegetation Models (DGVMs) typically only explore a range of socio-economically plausible pathways. In this study, we applied the state-of-the-art DGVM LPJmL to simulate the Amazon forest's response under idealized scenarios where precipitation is linearly decreased and subsequently increased between current levels and zero. Our results indicate a nonlinear but reversible relationship between vegetation Above Ground Biomass (AGB) and Mean Annual Precipitation (MAP), suggesting a threshold at a critical MAP value, below which vegetation biomass decline accelerates with decreasing MAP. We find that approaching this critical threshold is accompanied by critical slowing down, which can hence be expected to warn of accelerating biomass decline with decreasing rainfall. The critical precipitation threshold is lowest in the northwestern Amazon, whereas the eastern and southern regions may already be below their critical MAP thresholds. Overall, we identify the seasonality of precipitation and the potential evapotranspiration (PET) as the most important parameters determining the threshold value. While vegetation fires show little effect on the critical threshold and the biomass pattern in general, the ability of trees to adapt to water stress by investing in deep roots leads to increased biomass and a lower critical threshold in some areas in the eastern and southern Amazon where seasonality and PET are high. Our findings underscore the risk of Amazon forest degradation due to changes in the water cycle, and imply that regions that are currently characterized by higher water availability may exhibit heightened vulnerability to future drying.