LLMs can produce functionally correct programs, yet correctness alone does not guarantee reliability. Two programs passing the same tests can exhibit drastically different runtime behavior, creating hidden risks such as performance bottlenecks and memory leaks. Despite this, the runtime consistency of LLM-generated code remains largely unexplored. In this work, we introduce a framework to systematically quantify execution-time memory stability across multiple correct generations for the same task. We propose a novel solution-level metric, DMPD (Dynamic Mean Pairwise Distance), which uses Dynamic Time Warping to compare the shapes of memory usage profiles. These profiles, which we term Monotonic Peak Profiles (MPPs), are transformed to suppress transient noise, enabling robust comparison. By aggregating these scores, we derive a model-level Model Instability Score (MIS). Across the BigOBench and CodeContests benchmarks, we find substantial runtime divergence among correct solutions, revealing that instability often increases with higher sampling temperatures even as pass@1 improves. We also uncover exploratory correlations between our stability metrics and established software-engineering indicators (e.g., Cognitive and Cyclomatic Complexity), suggesting a link between operational behavior and code maintainability. These findings enable stability-aware selection of passing candidates in CI/CD pipelines, reducing operational risk without sacrificing correctness. Artifacts are available at https://github.com/pkrajput/memory_profiling.