Anaerobic digestion is considered a key technology for the future bio-based economy. The microbial consortium carrying out the anaerobic digestion process is quite complex, and its exact role in terms of "elasticity", i.e., the ability to rapidly adapt to changing conditions, is still unknown. In this study, the role of the initial microbial community in terms of operational stability and stress tolerance was evaluated during a 175-day experiment. Five different inocula from stable industrial anaerobic digesters were fed a mixture of waste activated sludge and glycerol. Increasing ammonium pulses were applied to evaluate stability and stress tolerance. A different response in terms of start-up and ammonium tolerance was observed among the different inocula. Methanosaetaceae were the dominant acetoclastic methanogens, yet, Methanosarcinaceae increased in abundance at elevated ammonium concentrations. A shift from a Firmicutes to a Proteobacteria dominated bacterial community was observed in failing digesters. Methane production was strongly positively correlated with Methanosaetaceae, but also with Bacteria related to Anaerolinaceae, Clostridiales, and Alphaproteobacteria. Volatile fatty acids were strongly positively correlated with Betaproteobacteria and Bacteroidetes, yet ammonium concentration only with Bacteroidetes. Overall, these results indicate the importance of inoculum selection to ensure stable operation and stress tolerance in anaerobic digestion.