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Recent foundational video-to-video diffusion models have achieved impressive results in editing user provided videos by modifying appearance, motion, or camera movement. However, real-world video editing is often an iterative process, where users refine results across multiple rounds of interaction. In this multi-turn setting, current video editors struggle to maintain cross-consistency across sequential edits. In this work, we tackle, for the first time, the problem of cross-consistency in multi-turn video editing and introduce Memory-V2V, a simple, yet effective framework that augments existing video-to-video models with explicit memory. Given an external cache of previously edited videos, Memory-V2V employs accurate retrieval and dynamic tokenization strategies to condition the current editing step on prior results. To further mitigate redundancy and computational overhead, we propose a learnable token compressor within the DiT backbone that compresses redundant conditioning tokens while preserving essential visual cues, achieving an overall speedup of 30%. We validate Memory-V2V on challenging tasks including video novel view synthesis and text-conditioned long video editing. Extensive experiments show that Memory-V2V produces videos that are significantly more cross-consistent with minimal computational overhead, while maintaining or even improving task-specific performance over state-of-the-art baselines. Project page: this https URL