Grounding is the collaborative process of establishing mutual belief sufficient for a communicative goal. While static grounding maps language to a shared context, dynamic grounding requires agents to negotiate meaning across turns. Current multi-agent Large Language Model (LLM) benchmarks largely emphasize static, one-shot tasks, overlooking whether agents can repair grounding breakdowns through interaction. We introduce an iterated multi-turn negotiation game where two agents allocate shared resources to private projects with verifiable jointly optimal outcomes. Although individual agents can identify Pareto-optimal allocations in isolation, agent dyads consistently fail to reach them across models. We identify four failure modes: (1) loss of shared interaction history, (2) stubborn anchoring to early proposals, (3) defaulting to equal splits over reward-maximizing coordination, and (4) referential binding errors across turns. Our baselines show that the coordination gap is not explained by individual reasoning limits or insufficient information exchange alone. Instead, the bottleneck lies in dynamic grounding: joint plan formation, commitment, and execution.