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Piezoelectricity is a tensor property of rank 3 that couples mechanical stress to electric polarization in non-centrosymmetric crystals. Accurate prediction of the piezoelectric tensor from atomic structure is essential for discovering new sensors, actuators, and energy-harvesting materials in data-driven materials engineering. Yet many researchers continue to apply invariant graph neural networks such as CGCNN, MEGNet, and SchNet—architectures originally designed for scalar properties like formation energy—to this tensor task. These models are rotationally invariant: their outputs remain unchanged under any reorientation of the crystal lattice. The piezoelectric tensor, however, must transform covariantly with orientation. As a direct consequence, invariant GNNs systematically predict zero piezoelectricity or near-zero random noise across entire datasets. This failure mode analysis identifies four core reasons: sign ambiguity arising from untracked orientation-dependent sign flips, component confusion caused by rotational permutation of tensor elements, symmetry overconstraint that forces unphysical relations across crystal classes, and vanishing off-diagonal components that average to zero under random rotations. The analysis draws exclusively on peer-reviewed literature in computational materials science and shows that equivariant GNNs are not merely an improvement but a strict necessity for any rank-2 or rank-3 tensor property. Detection principles and mitigation strategies are outlined conceptually, without reference to specific benchmarks or numerical scores. The work underscores a broader limitation in invariant architectures for tensorial phenomena in materials informatics and calls for their replacement by orientation-aware equivariant frameworks in future tensor property prediction pipelines.