Vision-Language Models (VLMs) are powerful yet computationally intensive for widespread practical deployments. To address such challenge without costly re-training, post-training acceleration techniques like quantization and token reduction are extensively explored. However, current acceleration evaluations primarily target minimal overall performance degradation, overlooking a crucial question: does the accelerated model still give the same answers to the same questions as it did before acceleration? This is vital for stability-centered industrial applications where consistently correct answers for specific, known situations are paramount, such as in AI-based disease diagnosis. We systematically investigate this for accelerated VLMs, testing four leading models (LLaVA-1.5, LLaVA-Next, Qwen2-VL, Qwen2.5-VL) with eight acceleration methods on ten multi-modal benchmarks. Our findings are stark: despite minimal aggregate performance drops, accelerated models changed original answers up to 20% of the time. Critically, up to 6.5% of these changes converted correct answers to incorrect. Input perturbations magnified these inconsistencies, and the trend is confirmed by case studies with the medical VLM LLaVA-Med. This research reveals a significant oversight in VLM acceleration, stressing an urgent need for instance-level stability checks to ensure trustworthy real-world deployment.