Controlling diversity in LLM-agent simulations is essential for balancing stability in structured tasks with variability in open-ended interactions. However, we observe that dialogue diversity tends to degrade over long-term simulations. To explore the role of prompt design in this phenomenon, we modularized the utterance generation prompt and found that reducing contextual information leads to more diverse outputs. Based on this insight, we propose Adaptive Prompt Pruning (APP), a novel method that allows users to control diversity via a single parameter, λ. APP dynamically prunes prompt segments based on attention scores and is compatible with existing diversity control methods. We demonstrate that APP effectively modulates diversity through extensive experiments and propose a method to balance the control trade-offs. Our analysis reveals that all prompt components impose constraints on diversity, with the Memory being the most influential. Additionally, high-attention contents consistently suppress output diversity.