Many e-commerce websites use recommender systems to recommend items to users. When a user or item is new, the system may fail because not enough information is available on this user or item. Various solutions to this `cold-start problem' have been proposed in the literature. However, many real-life e-commerce applications suffer from an aggravated, recurring version of cold-start even for known users or items, since many users visit the website rarely, change their interests over time, or exhibit different personas. This paper exposes the `Continuous Cold Start' (CoCoS) problem and its consequences for content- and context-based recommendation from the viewpoint of typical e-commerce applications, illustrated with examples from a major travel recommendation website, Booking.com.