Robots have the potential to revolutionize the way healthcare is delivered, particularly with regard to improving access to it. In-home robotic assistants could be used to extend care in a consistent, scalable, and personalized way. To realize this vision, we decompose the requirements of such a system, propose a target architecture, and illustrate where more research effort is needed. In particular, we focus on preference inference as a subproblem in which we aim to make direct progress. Current preference learning techniques lack the ability to infer long-term, task-independent preferences in realistic, interactive, incomplete-information settings. To address this gap, we introduce a novel preference-inference formulation, inspired by assistive robotics applications, in which a robot must infer these kinds of preferences based only on observing the user's behavior in various tasks. We then propose a candidate inference algorithm based on maximum-margin methods, and evaluate its performance in the context of robot-assisted prehabilitation. We find that the algorithm learns to predict aspects of the user's behavior as it is given more data, and that it shows strong convergence properties after a small number of iterations. This result moves us towards the vision of more helpful and personal in-home robotic assistants, and demonstrates the tractability of future progress in this area.