Recent years have seen transformative progress in machine comprehension and generation of human language, but maintaining thematic coherence and contextual continuity over extended interactions remains a significant hurdle. This paper introduces a novel framework for response generation, the Contextual Relevance Transfer (CRT) enabled by Continuity-Based Response Generation (CBRG), designed to address these challenges by retaining relevance and coherence across multiturn exchanges. CRT and CBRG work in tandem to embed context-specific relevance patterns into large language model architectures, thereby supporting more fluid and thematically aligned interactions. By implementing CRT within an opensource LLM, this research evaluates the capacity for CBRG to facilitate continuity without sacrificing computational efficiency, employing context-sensitive filters, adaptive protocols, and recursive relevance loops. Empirical results illustrate notable advancements in multi-turn coherence, sentiment alignment, and topic transition smoothness, showing CBRG's effectiveness in minimizing response degeneration and supporting a more cohesive user experience. Experimental benchmarks confirm that CBRG not only achieves high continuity scores but also demonstrates reduced response latency, making it viable for realtime conversational applications. The insights offered here reveal the potential for contextually aware frameworks like CBRG to redefine interaction quality in intelligent language-based systems, presenting new possibilities for applications requiring sustained engagement and thematic accuracy.