Serving large language models under latency service-level objectives (SLOs) is a configuration-heavy systems problem with an unusually failure-prone search space: many plausible configurations crash outright or miss user-visible latency targets, and standard black-box optimizers treat these failures as wasted trials. We present SLO-Guard, a crash-aware autotuner for vLLM serving that treats crashes as first-class observations. SLO-Guard combines a feasible-first Thermal Budget Annealing (TBA) exploration phase with a warm-started Tree-structured Parzen Estimator (TPE) exploitation phase; the handoff replays all exploration history, including crashes encoded as extreme constraint violations. We additionally contribute a configuration-repair pass, a GPU-aware KV-cache memory guard, and a four-category crash taxonomy. We evaluate SLO-Guard on Qwen2-1.5B served with vLLM 0.19 on an NVIDIA A100 40GB. Across a pre-specified five-seed study, both SLO-Guard and uniform random search attain 75/75 feasibility with zero crashes under the corrected concurrent harness, and are statistically tied on best-achieved latency (Mann-Whitney two-sided p=0.84). SLO-Guard's advantage is in budget consistency: more trials in the fast-serving regime (10.20 vs. 7.40 out of 15; one-sided p=0.014) and higher post-handoff consistency (0.876 vs. 0.539; p=0.010). Under concurrent load, SLO-Guard's cross-seed standard deviation on best latency is 4.4x tighter than random search's (2.26 ms vs. 10.00 ms). A harness-replication analysis shows that the consistency findings survive an independent sequential-dispatch measurement condition. The central claim is not that SLO-Guard finds a better final configuration, but that it spends a fixed tuning budget more predictably once the fast regime has been found.