Effective collaboration requires groups to strategically regulate themselves to overcome challenges. Research has shown that groups may fail to regulate due to differences in members' perceptions of challenges which may benefit from external support. In this study, we investigated the potential of leveraging three distinct natural language processing models: an expert knowledge rule-based model, a supervised machine learning (ML) model and a Large Language model (LLM), in challenge detection and challenge dimension identification (cognitive, metacognitive, emotional and technical/other challenges) from student discourse, was investigated. The results show that the supervised ML and the LLM approaches performed considerably well in both tasks, in contrast to the rule-based approach, whose efficacy heavily relies on the engineered features by experts. The paper provides an extensive discussion of the three approaches' performance for automated detection and support of students' challenge moments in collaborative learning activities. It argues that, although LLMs provide many advantages, they are unlikely to be the panacea to issues of the detection and feedback provision of socially shared regulation of learning due to their lack of reliability, as well as issues of validity evaluation, privacy and confabulation. We conclude the paper with a discussion on additional considerations, including model transparency to explore feasible and meaningful analytical feedback for students and educators using LLMs.