Table-based question answering requires complex reasoning capabilities that current LLMs struggle to achieve with single-pass inference. Existing approaches, such as Chain-of-Thought reasoning and question decomposition, lack error detection mechanisms and discard problem-solving experiences, contrasting sharply with how humans tackle such problems. In this paper, we propose MAPLE (Multi-agent Adaptive Planning with Long-term mEmory), a novel framework that mimics human problem-solving through specialized cognitive agents working in a feedback-driven loop. MAPLE integrates 4 key components: (1) a Solver using the ReAct paradigm for reasoning, (2) a Checker for answer verification, (3) a Reflector for error diagnosis and strategy correction, and (4) an Archiver managing long-term memory for experience reuse and evolution. Experiments on WiKiTQ and TabFact demonstrate significant improvements over existing methods, achieving state-of-the-art performance across multiple LLM backbones.