Short-term prospective time estimation is an important part of many tasks and there is a large body of research on the topic. However, the relationship between time awake and time estimation performance is unclear due to mixed and conflicting results. This paper focuses on two studies: one that provides evidence of a relationship between time estimation performance and time awake, and one that does not. In the former, the task required participants to estimate 10s time intervals, while the latter used a motion extrapolation paradigm. Using computational cognitive models, we implemented a mechanism to fatigue the timing module in ACT-R, which leads to one possible explanation for contrasting results in these two task paradigms.