Chronic illness often goes hand-in-hand with absence from school, and students miss out on learning opportunities at school for extended or accumulative periods of time. Many young people seek to continue their school studies nonetheless. The need to consider viable ways to support them academically arose in the context of a project called "Link 'n Learn" funded by an Australian Research Council Linkage grant (2008--2010). This paper reports on one aspect of the project -- an in-depth qualitative case study of 22 participants: senior secondary students with diverse types of chronic illness who were continuing their studies during absence from school and their mathematics teachers. The study found that the students' concerns centred on academic issues -- their perceived need for support from and interaction with their teachers. The teachers' concerns focused on medical issues -- their students having to manage illness. Facilitators of these students' ability to continue studying included their ambition, perseverance with independent learning, initiative in seeking help, and quick recovery from medical treatment cycles. Teacher-related facilitators included the teachers' willingness to interact using communication media, confidence in initiating contact, and ability to modify their students' learning programme. Other facilitators included a responsive school technology department, technology tutoring from students, and the involvement of family members or tutors. Outcomes for students and teachers of their interactions with each other during lengthy periods of absence, and implications for schools, are discussed.