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The scaffolding problem represents a critical yet underrecognized failure mode in artificial intelligence for materials science, wherein seemingly autonomous AI systems depend on vast, unstated layers of scientific infrastructure that remain invisible until they fail. At this point, the AI models themselves cease to function reliably or reproducibly. This failure mode arises because materials AI pipelines are not standalone artifacts but are instead supported by extensive scaffolding—databases, software ecosystems, computational resources, measurement standards, tacit community knowledge, and institutional frameworks—that enable data ingestion, model training, and inference but are rarely documented or maintained as core components of the research. The scaffolding problem is formally defined as the failure to recognize, document, and sustain these invisible support structures, leading to unrecognized vulnerabilities that undermine the reliability of data-driven discoveries in materials design. Materials AI depends on six distinct types of scientific infrastructure, ranging from data repositories such as the Materials Project and AFLOW to software libraries like pymatgen and institutional funding mechanisms, each of which carries hidden assumptions about stability and accessibility. Scaffolding failures occur through mechanisms including infrastructure decay, dependency drift, access loss, and knowledge erosion, producing a typology of four specific failure modes: silent dependency failure, reproducibility collapse, infrastructure lock-in, and knowledge gap failure. Detection relies on systematic dependency mapping, version pinning, access monitoring, reproduction testing, and knowledge auditing, while mitigation demands explicit documentation, containerization, data archiving, dependency minimization, infrastructure independence, and knowledge capture. By articulating the scaffolding problem as a distinct failure mode, this analysis reveals how unexamined infrastructure dependencies threaten the long-term viability of materials AI and calls for a fundamental shift toward treating scaffolding as an explicit, first-class concern in research practice.