Large language models (LLMs) are increasingly used in research as both tools and objects of study. Much of this work assumes that LLM performance under fixed conditions (identical model snapshot, hyperparameters, and prompt) is time-invariant, meaning that average output quality remains stable over time; otherwise, reliability and reproducibility would be compromised. To test the assumption of time invariance, we conducted a longitudinal study of GPT-4o's average performance under fixed conditions. The LLM was queried to solve the same physics task ten times every three hours over approximately three months. Spectral (Fourier) analysis of the resulting time series revealed substantial periodic variability, accounting for about 20% of total variance. The observed periodic patterns are consistent with interacting daily and weekly rhythms. These findings challenge the assumption of time invariance and carry important implications for research involving LLMs.