The conventional discourse on existential risks (x-risks) from AI typically focuses on abrupt, dire events caused by advanced AI systems, particularly those that might achieve or surpass human-level intelligence. These events have severe consequences that either lead to human extinction or irreversibly cripple human civilization to a point beyond recovery. This discourse, however, often neglects the serious possibility of AI x-risks manifesting incrementally through a series of smaller yet interconnected disruptions, gradually crossing critical thresholds over time. This paper contrasts the (...) conventional "decisive AI x-risk hypothesis" with an "accumulative AI x-risk hypothesis". While the former envisions an overt AI takeover pathway, characterized by scenarios like uncontrollable superintelligence, the latter suggests a different causal pathway to existential catastrophes. This involves a gradual accumulation of critical AI-induced threats such as severe vulnerabilities and systemic erosion of economic and political structures. The accumulative hypothesis suggests a boiling frog scenario where incremental AI risks slowly converge, undermining societal resilience until a triggering event results in irreversible collapse. Through systems analysis, this paper examines the distinct assumptions differentiating these two hypotheses. It is then argued that the accumulative view can reconcile seemingly incompatible perspectives on AI risks. The implications of differentiating between these causal pathways --- the decisive and the accumulative --- for the governance of AI as well as long-term AI safety are discussed. (shrink)