Today's rapidly advancing technologies and highly competitive and dynamic markets make continuity essential in organizations' service development and innovation activities. However, little is known about why and how organizations organize for continuous digital service innovation (DSI) and what follows. To address this gap, this paper explores the "why," "how," and "what" of continuous DSI. We present findings from a thematic analysis of 23 semi-structured interviews with six case organizations to shed light on the external and internal drivers (why), principles, practices, methods (how), and outcomes (what) of continuous DSI for organizations. We observe that, externally, continuous DSI is driven by the rapid and dynamic changes in the business environment, rapid technological advancements, and customers' expectations of continuity. Multiple customer, profitability, performance, and technology-related objectives exist internally. The organization for continuous DSI emphasizes customer- and other stakeholder-related principles and practices, as well as continuity-related principles and practices for the development and innovation activities. In addition, we find that service organizations implement various methods for continuous DSI. The effects of continuous DSI on organizations include diverse customer, development and innovation, communication, and collaboration-related outcomes. We contribute by offering a novel, practice-based understanding of continuous DSI in organizations, which may inform future research on this emerging phenomenon.