Non-functional requirements (NFR), which include performance, availability, and maintainability, are vitally important to overall software quality. However, research has shown NFRs are, in practice, poorly defined and difficult to verify. Continuous software engineering practices, which extend agile practices, emphasize fast paced, automated, and rapid release of software that poses additional challenges to handling NFRs. In this multi-case study we empirically investigated how three organizations, for which NFRs are paramount to their business survival, manage NFRs in their continuous practices. We describe four practices these companies use to manage NFRs, such as offloading NFRs to cloud providers or the use of metrics and continuous monitoring, both of which enable almost real-time feedback on managing the NFRs. However, managing NFRs comes at a cost as we also identified a number of challenges these organizations face while managing NFRs in their continuous software engineering practices. For example, the organizations in our study were able to realize an NFR by strategically and heavily investing in configuration management and infrastructure as code, in order to offload the responsibility of NFRs; however, this offloading implied potential loss of control. Our discussion and key research implications show the opportunities, trade-offs, and importance of the unique give-and-take relationship between continuous software engineering and NFRs. Research artifacts may be found at https://doi.org/10.5281/zenodo.3376342.