Multi-omics analytics can integrate genomic, transcriptomic, epigenomic, proteomic, metabolomic, and related data into richer representations of biological systems, but analytical flexibility can also make strong results sensitive to defensible changes in preprocessing, integration, validation, or context. This paper examines that problem as reproducibility risk at the decision level. We combine a structured narrative synthesis of multi-omics methodology, computational reproducibility, biomedical machine learning governance, and organizational decision research with an illustrative Monte Carlo stress test. We define the Analytical Fragility Index (AFI) as the proportion of decision outputs that change across pre-specified plausible perturbations. In 500 simulated experiments with three omics signal layers, increasing technical confounding made an internally selected pipeline look progressively stronger while becoming less transportable. At the highest confounding level, mean development Area Under The Receiver Operating Characteristic Curve (AUROC) reached 0.978, replication AUROC fell to 0.753, the optimism gap reached 0.225, and 29.8% of binary decisions changed after technical context shift. These are illustrative rather than empirical estimates. We therefore propose six risk-based evidence gates linking provenance, design alignment, validation, stress testing, independent challenge, and post-decision learning. The implication is that multi-omics programs should manage analytical quality by the stability and consequence of decisions, not by model accuracy alone.