Multimodal large language models (MLLMs) perform strongly on isolated spatial tasks, but whether their predictions remain persistent and mutually coherent across viewpoints and competing scenes is unclear. We formalize this behavioral property as spatial-state integrity and introduce CVT-Bench, a factorial diagnostic suite spanning two domains (CVT-Synthetic, CVT-Real), four context regimes (CVT-Isolated, irrelevant filler, attribute filler, CVT-Competing), three representations (Image, Text/BBox, Scene Graph), and ten viewpoint conditions (nine azimuths from $0^\circ$ to $360^\circ$ at $45^\circ$ increments, plus Top) with target views withheld. Across 200 scenes and 11,833 relational queries, we measure counterfactual accuracy, cycle consistency, the normalized survival coefficient, spatial realizability, and context-specific interference. Five state-of-the-art MLLMs exhibit rapid persistence loss and frequently produce jointly unrealizable states despite high local accuracy, with failures amplified by competing contexts and natural-scene complexity. Matched irrelevant and attribute filler controls show that prompt length, position, or loss of scene access alone are insufficient explanations. On average, Text/BBox improves accuracy, persistence, and realizability, while Scene Graph provides complementary gains; neither eliminates the instability. Thus, isolated spatial accuracy substantially overestimates robustness, establishing spatial-state integrity as a distinct evaluation target. The complete benchmark and codebase will be publicly released.

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