The Fragility Index (FI) has become a widely cited measure of statistical robustness in clinical trials, yet its computation often fails under Fisher’s exact test constraints. This paper systematically demonstrates that the FI is mathematically unattainable across a broad range of realistic clinical scenarios—including rare events, balanced small samples, and extreme imbalances—using 14 representative 2×2 contingency tables. Alternative fragility metrics, including the Percent Fragility Index (PFI), Relative Risk Index (RRI), Risk Quotient (RQ), and Robustness Index (RI), were evaluated for computational success and interpretability. The FI failed in 100% of test cases, while PFI and RQ achieved universal computability (100%) and provided clinically meaningful interpretations. The RQ, in particular, quantifies distance from therapeutic neutrality on a bounded 0–1 scale and avoids dependence on statistical significance thresholds. These findings reveal that the FI itself is fragile, supporting a transition toward universally computable and clinically interpretable fragility metrics such as PFI and RQ.