Evaluating the programming robustness of large language models (LLMs) is paramount for ensuring their reliability in AI-based software development. However, adversarial attacks exhibit fundamental limitations that compromise fair robustness assessment: they demonstrate contradictory evaluation outcomes where different attack strategies tend to favor different models, and more critically, they operate solely through external perturbations, failing to capture the intrinsic stability essential for autonomous coding agents where subsequent inputs are endogenously generated by the model itself. We introduce EVALOOOP, a novel assessment framework that evaluates robustness from a self-consistency perspective, leveraging the natural duality inherent in software engineering tasks (e.g., code generation and code summarization). EVALOOOP establishes a self-contained feedback loop where an LLM iteratively transforms between code and natural language until functional failure occurs, with robustness quantified by a novel Average Sustainable Loops (ASL) metric-the mean number of iterations maintaining functional correctness across benchmark tasks. This cyclical strategy intrinsically evaluates robustness without relying on external attack configurations, providing a unified metric that reveals how effectively LLMs preserve semantic integrity through sustained self-referential transformations. We evaluate 96 popular LLMs, ranging from 0.5B to 685B parameters, on EVALOOOP equipped with the MBPP Plus benchmark, and found that EVALOOOP typically induces a 2.65%-47.62% absolute drop in pass@1 accuracy within ten loops. Intriguingly, robustness does not always align with initial performance (i.e., one-time query); for instance, Qwen3-235B-A22B-Instruct-2507, despite inferior initial code generation compared to OpenAI's o-series models and DeepSeek-V3, demonstrated the superior robustness (ASL score).