Multimodal Large Language Models (MLLMs) have demonstrated strong capabilities across a wide range of vision language tasks. However, when applied to large scale image classification, their performance degrades significantly as the label space expands a phenomenon we define as Performance Collapse in Long Sequence Recognition. Through an information theoretic analysis, we reveal that this collapse stems from a fundamental conflict between the escalating information entropy and the prominent attention dilution and decay within attention mechanisms, which impairs the model's ability to maintain a sufficient signal-to-noise ratio when processing extremely long prompts. To mitigate this, we propose Divide-and-Conquer Inference (DCI), a novel test-time scaling strategy for visual recognition with MLLMs. DCI recursively decomposes complex global classification tasks into multiple simpler, localized subproblems and employs a dynamic pruning mechanism to compress the search space. This method effectively improves the local signal to noise ratio and model accuracy by mitigating the inherent weight dilution issues in long-sequence inference. Moreover, while traditional self-attention incurs a prohibitive quadratic computational complexity, DCI achieves more favorable scaling behavior and substantially accelerates inference in large scale classification scenarios. Extensive experiments on benchmarks such as ImageNet-1K and ImageNet-21K demonstrate that DCI consistently improves classification accuracy. This enables lightweight open-source models to rival or even surpass frontier closed-source giants without any additional training or fine-tuning. As a model-agnostic, plug-and-play paradigm, DCI offers an efficient approach for scaling the inferential precision of MLLMs in large-scale scenarios.