A student's short-term study behavior may not necessary infer his/her long-term behavior. It is very common to see a student changes study strategy throughout a semester and adapts to learning condition. For example, a student may work very hard before the first exam but gradually reducing the effort due to several possible reasons, e.g., being overwhelmed by various course work or discouraged by increasing complexity in the subject. Consistency or differences of one student's behavior is more likely to be discovered by multiple granularity of learning analytics. In this study, we investigate students' study persistence on a self-assessment platform and explore how such a behavioral pattern is related to the performance in exams. A probabilistic mixture model trained by response streams of log data is applied to cluster students' behavior into persistence patterns, which are further categorized into micro (short-term) and macro (long-term) patterns according to the span of time being modeled. We found four types of micro persistence patterns and several macro patterns in the analysis and analyzed their relations with exam performances. The result suggests that the consistency of persistence patterns can be an important factor driving student's overall performance in the semester, and students achieving higher exam scores show relatively persistent behavior compared to students receiving lower scores.