Customer-service question answering (QA) systems increasingly rely on conversational language understanding. While Large Language Models (LLMs) achieve strong performance, their high computational cost and deployment constraints limit practical use in resource-constrained environments. Small Language Models (SLMs) provide a more efficient alternative, yet their effectiveness for multi-turn customer-service QA remains underexplored, particularly in scenarios requiring dialogue continuity and contextual understanding. This study investigates instruction-tuned SLMs for context-summarized multi-turn customer-service QA, using a history summarization strategy to preserve essential conversational state. We also introduce a conversation stage-based qualitative analysis to evaluate model behavior across different phases of customer-service interactions. Nine instruction-tuned low-parameterized SLMs are evaluated against three commercial LLMs using lexical and semantic similarity metrics alongside qualitative assessments, including human evaluation and LLM-as-a-judge methods. Results show notable variation across SLMs, with some models demonstrating near-LLM performance, while others struggle to maintain dialogue continuity and contextual alignment. These findings highlight both the potential and current limitations of low-parameterized language models for real-world customer-service QA systems.