Traditional benchmarks for large language models (LLMs) primarily assess safety risk through breadth-oriented evaluation across diverse tasks. However, real-world deployment exposes a different class of risk: operational failures arising from repeated inference on identical or near-identical prompts rather than broad task generalization. In high-stakes settings, response consistency and safety under sustained use are critical. We introduce Accelerated Prompt Stress Testing (APST), a depth-oriented evaluation framework inspired by reliability engineering. APST repeatedly samples identical prompts under controlled operational conditions (e.g., decoding temperature) to surface latent failure modes including hallucinations, refusal inconsistency, and unsafe completions. Rather than treating failures as isolated events, APST models them as stochastic outcomes of independent inference events. We formalize safety failures using Bernoulli and binomial models to estimate per-inference failure probabilities, enabling quantitative comparison of reliability across models and decoding configurations. Applying APST to multiple instruction-tuned LLMs evaluated on AIR-BENCH-derived safety prompts, we find that models with similar benchmark-aligned scores can exhibit substantially different empirical failure rates under repeated sampling, particularly as temperature increases. These results demonstrate that shallow, single-sample evaluation can obscure meaningful reliability differences under sustained use. APST complements existing benchmarks by providing a practical framework for evaluating LLM safety and reliability under repeated inference, bridging benchmark alignment and deployment-oriented risk assessment.