A significant portion of student programming submissions in CS1 learning environments are uncompilable, limiting their use in student modeling and downstream knowledge tracing. Traditional modeling pipelines often exclude these cases, discarding observations of student learning. This study investigates automated program repair as a strategy to recover uncompilable code while preserving students' structural intent for use in student modeling. Within this framework, we assess large language models (LLMs) as repair agents under high- and low-context prompting conditions. Repairs were evaluated for compilability, edit distance, and preservation of students' original structure and logic. While all models produced compilable repairs, they differed in how well they preserve students' control flow and code structure, affecting their pedagogical utility. By recovering uncompilable submissions, this work enables richer and more comprehensive analyses of learners' coding processes and development over time.