arXiv:2611.13412v1 Announce Type: new Abstract: LLM agents drive inference engines with closed-loop sessions whose context grows every turn, and serving them economically depends on prefix caching: a hit costs an incremental prefill of about a thousand tokens, a miss recomputes a 10--40K-token context. We show that this makes prefix-cached agent serving metastable. With an identical base workload, a few minutes of extra arrivals leaves a vLLM server in a degraded regime--a ~10% hit ratio, about half the throughput, and a backlog that grows for the remaining 70 minutes--while its no-burst twin stays healthy (9 of 12 pairs; none in the reverse direction). The regime appears at loads the cache-warm server sustains, is absent without prefix caching, and also appears with Qwen3-32B on SWE-bench agent trace shapes and on SGLang, which tolerates larger triggers. Slower service keeps more sessions in the system, their working set outgrows the KV pool, and every turn becomes a recomputation; a first-order workload-balance condition, calibrated independently, brackets when the regime can drain. Getting out is the harder problem: throttling new admissions recovered 1 of 7 matched collapsed runs, while suspending admitted sessions against a capacity-based limit recovered all of them within minutes. A CPU offload tier delays the collapse but does not prevent it. A budgeter that bounds the resident KV demand of active sessions to the pool, with thresholds that need no per-workload tuning, prevented the failure in every run we tested.