Large Language Models (LLMs) demonstrate strong reasoning capabilities but struggle with hallucinations and limited transparency. Recently, KG-enhanced LLMs that integrate knowledge graphs (KGs) have been shown to improve reasoning performance, particularly for complex, knowledge-intensive tasks. However, these methods still face significant challenges, including inaccurate retrieval and reasoning failures, often exacerbated by long input contexts that obscure relevant information or by context constructions that struggle to capture the richer logical directions required by different question types. Furthermore, many of these approaches rely on LLMs to directly retrieve evidence from KGs, and to self-assess the sufficiency of this evidence, which often results in premature or incorrect reasoning. To address the retrieval and reasoning failures, we propose ProgRAG, a multi-hop knowledge graph question answering (KGQA) framework that decomposes complex questions into sub-questions, and progressively extends partial reasoning paths by answering each sub-question. At each step, external retrievers gather candidate evidence, which is then refined through uncertainty-aware pruning by the LLM. Finally, the context for LLM reasoning is optimized by organizing and rearranging the partial reasoning paths obtained from the sub-question answers. Experiments on three well-known datasets demonstrate that ProgRAG outperforms existing baselines in multi-hop KGQA, offering improved reliability and reasoning quality.