The intersection between security and continuous software engineering has been of great interest since the early years of the agile development movement, and it remains relevant as software development processes are more frequently guided by agility and the adoption of DevOps. Several authors have contributed studies about the framing of secure agile development and secure DevOps, motivating academic contributions to methods and practices, but also discussions around benefits and challenges. Especially the challenges captured also our interest since, for the last few years, we are conducting research on secure continuous software engineering from a more applied, practical perspective with the overarching aim to introduce solutions that can be adopted at scale. The short positioning at hands summarizes a relevant part of our endeavors in which we validated challenges with several practitioners of different roles. More than framing a set of challenges, we conclude by presenting four key research directions we identified for practitioners and researchers to delineate future work.