Quantifying tail risk in structural mechanics is essential for reliability-driven design, yet remains computationally prohibitive for high-dimensional problems involving spatially correlated uncertainty. Accurate evaluation of tail-sensitive response measures requires resolving rare but extreme events, leading to excessive computational cost when classical Monte Carlo methods are coupled with high-fidelity finite element models. This work presents a quantum-enhanced framework for tail-risk estimation in stochastic structural mechanics based on a stabilized maximum-likelihood variant of iterative quantum amplitude estimation (IQAE) [1]. By reformulating tail-risk evaluation as a bounded expectation of a normalized hinge function, the problem is reduced to quantum amplitude estimation while preserving a mechanically consistent interpretation. To ensure robustness under finite-shot noise and the non-injective oscillatory behavior induced by Grover amplification, the proposed method integrates likelihood-constrained interval tracking, multi-hypothesis feasibility management, periodic low-depth disambiguation, and an explicit failure-probability budget. This stabilization strategy preserves the quadratic oracle-complexity advantage of amplitude estimation while providing rigorous finite-sample confidence guarantees. The approach is demonstrated on stochastic finite element benchmarks with spatially correlated material uncertainty. Numerical results show that the proposed method achieves substantially lower oracle complexity and reduced estimator variance compared to classical Monte Carlo estimation at comparable confidence levels, while maintaining global statistical reliability. These results establish a practically viable and theoretically grounded quantum-assisted workflow for tail-risk quantification in continuum mechanics and provide one of the first systematic benchmarks coupling correlated random fields, full finite element analysis, and stabilized quantum inference for structural reliability assessment.