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Sequential learning is increasingly invoked in compositionally complex alloy modeling because the combinatorial scale of alloy design space, coupled with the cost of density-functional theory calculations and the staged nature of data acquisition, makes exhaustive one-shot training impractical. Yet under these conditions, neural networks are prone to catastrophic forgetting, whereby adaptation to newly introduced compositions, phases, or thermodynamic regimes degrades performance on previously learned ones. This article examines the conditions under which such failure emerges in compositionally complex alloys and shows that forgetting is not incidental but structurally induced by the interaction of shared representations, non-linear property landscapes, high compositional dimensionality, and sparse task-specific data. The analysis identifies four recurrent failure modes—elemental forgetting, concentration range collapse, phase space amnesia, and temperature-induced overwrite—and links them to underlying mechanisms of parameter interference, representation drift, output distribution shift, and gradient conflict. It further delineates the conditions that intensify these dynamics, including high compositional similarity, abrupt task transitions, rehearsal-free updates, and unstable optimization settings. By integrating detection criteria with mitigation strategies such as elastic weight consolidation, memory replay, modular architectures, and curriculum sequencing, the study provides a practical and conceptual framework for continual learning in alloy discovery. The central argument is that robust sequential learning in compositionally complex alloys requires forgetting-aware design at the levels of evaluation, architecture, and training protocol if materials machine learning is to support reliable lifelong modeling across expanding compositional spaces.