Reorganization processes in dense active matter remain a central open question in nonequilibrium physics. In particular, how persistent self-propulsion drives local rearrangements and triggers collective failure events is not well understood. Here, we investigate such activity-induced rearrangements, which can cascade into avalanches, in a dense assembly of self-propelled particles. In the limit of large persistence time, these systems evolve through abrupt transitions between mechanically stable configurations, giving rise to rich intermittent behaviour. Using large-scale simulations of this activity-driven dynamics (ADD), we systematically characterize avalanche statistics across a range of system sizes and activity protocols. We quantify the scaling properties of avalanche-size distributions for two widely studied active matter models: active Brownian particles and active Ornstein-Uhlenbeck particles. By comparing these classes of dynamics, we identify how the nature of the propulsion mechanism influences the exponents associated with avalanche size distribution, as well as the frequency and temporal organization of avalanches. Comparisons with avalanches in quasistatic active flow (AQRD) and their analogues under quasistatic shear flow shed further light on the underlying physical commonalities and differences.