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This theoretical study establishes a materials-specific depth limit for graph neural networks used in crystal property prediction by showing that early-layer gradient norms decay as ρ raised to the remaining propagation depth, where ρ denotes the spectral radius of the normalized message-passing operator. Because ρ remains strictly below unity for connected crystal graphs, repeated aggregation induces exponential attenuation of backward signals and renders optimization ineffective beyond a critical number of layers. For representative crystal topologies with ρ ≈ 0.9, the practically trainable regime contracts to roughly 10–20 layers, well below the depth that would be required to resolve genuinely long-range order in large unit cells, defective lattices, or disordered materials. The bound follows directly from spectral decomposition and therefore holds independently of weight initialization and, at the leading-order level, independently of activation choice. The analysis further distinguishes vanishing gradients from over-smoothing, clarifies how coordination environment, connectivity, normalization, graph size, and symmetry reshape the depth ceiling, and situates the result within the broader theoretical literature on recurrent networks and graph learning. The central implication is that depth cannot be treated as a universally beneficial scaling axis in materials GNNs. Instead, reliable model design requires spectrally informed architectural choices, including residual pathways, adaptive depth control, and shallow message passing combined with explicit long-range representations. By linking crystal graph topology to backward propagation dynamics, this work provides a rigorous theoretical basis for depth-aware model design in computational materials discovery.