Long-horizon autonomous agents suffer from semantic livelock: they continue generating tokens and calling tools without making progress. Unlike a crash, this "zombie" state consumes API budget and time while remaining operationally active. We treat this as a progress violation and propose the Convergence Monitor, a light-weight sidecar that fingerprints agent states in embedding space. In a forensic analysis of real-world failures (SWE-agent corpus), we identified that 25% of the analyzed long-duration failures exhibited semantic livelock patterns. In one extreme case, an agent wasted 208 steps in a checkerboard oscillation pattern invisible to standard string-matching repetition guards. We argue that future Agentware requires a "liveness coprocessor" to ensure software makers do not pay for stalled execution.