Burnout is commonly associated with professions that entail a high rate of close relationships with other individuals or groups. This paper explores the association between burnout and interpersonal relationships using a relational, social network framework. We collected data on advice-seeking relationships among 102 teachers and administrative staff from a secondary school in Melbourne, Australia. Burnout was measured using the Burnout Assessment Tool and we focused on four core subscales: (1) exhaustion; (2) mental distance; (3) emotional impairment; and (4) cognitive impairment. We applied a particular class of statistical model for social networks called Exponential Random Graph Models (ERGMs) to shed new light on how level of burnout relates to formation of advice relations among school staff. Results indicated that high levels of overall burnout were linked to a higher number of advice-seeking ties among school staff. Additionally, teachers who scored high in cognitive impairment (i.e., difficulties in thinking clearly and learn new things at work) tended to seek and to provide advice to a greater number of others. Finally, school staff who scored high in exhaustion (i.e., a severe loss of energy that results in feelings of both physical and mental exhaustion) tended to be sought out less as advisors to others, while those high in mental distance (i.e., psychologically distancing oneself from others) were generally less likely to seek advice from other school staff. We discuss these findings drawing on Conservation of Resource theory. Notably, our results show that burnout is not only an individual-level problem, but that burnout is associated with reduced social connectivity in specific ways that may impact on how other school staff collaborate, culminating in a staff-wide overall impact that affects how schools function.