LLM judges have become central to model evaluations, online grading, and reward modeling. However, their accuracy on golden data does not guarantee stability under re-prompting, challenge, or sustained pushback. We introduce the Wiggle Framework, a unified stress test for epistemic stability in LLM judges. The framework assesses judge robustness along three dimensions: Mechanical Consistency (stability under re-prompting and reframing), Single-turn Conviction (stability under a single challenge), and Multi-turn Persistence (stability under sustained or adaptive pressure). Applying this framework to 9 frontier models across 14 judging tasks, we find that every model exhibits substantial wiggle, flipping verdicts 25-71% of the time under static pushback and 62-91% with an adversarial LLM persuader. Critically, pressure that succeeds in changing a judge's verdict is almost always net-corrupting with respect to ground truth. Beyond the framework, we identify baseline jury majority strength as the most effective single-shot signal for anticipating which items wiggle. This study provides the first apples-to-apples cross-dataset comparison of mechanical, conformity, and persuadability tests in a judging context. Blogger's Review: The Wiggle Framework introduced in this paper offers a powerful tool for assessing the stability of LLM judges, revealing the vulnerability of current models under pressure and challenge. This assessment is crucial for enhancing the reliability and safety of LMs in practical applications.