Large language models (LLMs) have shown great potential in multi-disciplinary team (MDT) medical consultations. However, long, multi-round, multi-role interaction trajectories inevitably lead to severe information dilution and context window overload, triggering context collapse which destabilizes reasoning. Furthermore, prior systems typically rely on unstructured trajectory history storage without structurally distilling key information or reflecting on errors, severely limiting continuous learning capabilities. We propose MDTeamGPT, a context-resilient and self-evolving multi-agent framework. Mechanistically, we introduce a specialized Lead Physician mechanism combined with a Residual Context architecture to compress and reorganize multi-round consensus, effectively mitigating context overload and reducing computational costs. For memory, we design a Dual Knowledge Base system comprising a CorrectKB for verified trajectories and a ChainKB for reflective error analysis, enabling self-evolution via retrieval from both successes and failures. We evaluated our framework on standard text datasets (MedQA, PubMedQA), multimodal benchmarks (VQA-RAD, SLAKE), and collected more complex clinical problems. Experimental results show that MDTeamGPT substantially outperforms existing baselines across both text-based and multimodal tasks, while also demonstrating superior diagnostic performance and stability in complex clinical scenarios.