Computer-aided design (CAD) has become indispensable to increasingly collaborative hardware design processes. Despite the long-standing and growing need for collaboration with CAD models and tools, anecdotal reports and ongoing researcher efforts point to a complex and unresolved set of challenges faced by designers when working with distributed CAD. We aim to close this academic-practitioner knowledge gap through the first systematic study of professional user-driven CAD collaboration challenges. In this work, we conduct semi-structured interviews with 20 CAD professionals of diverse industries, roles, and experience levels to understand their collaborative workflows with distributed CAD tools. In total, we identify 14 challenges related to collaborative design, communication, data management, and permissioning that are currently impeding effective collaboration in professional CAD teams. Our systematic classification of CAD collaboration challenges presents a guide for pressing areas of future work, highlighting important implications for CAD researchers, practitioners, and tool builders to target new advancement in CAD infrastructure, management choices, and modelling best practices. With the insights gained from this work, we hope to ultimately improve collaboration efficiency, quality, and innovation for future product design teams.