Multi-agent systems (MASs) have emerged as a promising paradigm for automated code generation, demonstrating impressive performance on established benchmarks. Despite their prosperous development, the fundamental mechanisms underlying their robustness remain poorly understood, raising critical concerns for real-world deployment. This paper conducts a systematic empirical study to uncover the internal robustness flaws of MASs using a mutation-based methodology. By designing a testing pipeline incorporating semantic-preserving mutation operators and a novel fitness function, we assess mainstream MASs across multiple datasets and LLMs. Our findings reveal substantial robustness flaws: semantically equivalent inputs cause drastic performance drops, with MASs failing to solve 7.9\%--83.3\% of problems they initially resolved successfully. Through comprehensive failure analysis, we discover a fundamental cause underlying these robustness issues: the \textit{planner-coder gap}, which accounts for 75.3\% of failures. This gap arises from information loss in the multi-stage transformation process where planning agents decompose requirements into underspecified plans, and coding agents subsequently misinterpret intricate logic during code generation. Based on this formulated information transformation process, we propose a \textit{repairing method} that mitigates information loss through multi-prompt generation and introduces a monitor agent to bridge the planner-coder gap. Evaluation shows that our repairing method effectively enhances the robustness of MASs by solving 40.0\%--88.9\% of identified failures. Our work uncovers critical robustness flaws in MASs and provides effective mitigation strategies, contributing essential insights for developing more reliable MASs for code generation.