Intelligent and reliable task planning is a core capability for generalized robotics, requiring a descriptive domain representation that sufficiently models all object and state information for the scene. We present CLIMB, a continual learning framework for robot task planning that leverages foundation models and execution feedback to guide domain model construction. CLIMB can build a model from a natural language description, learn non-obvious predicates while solving tasks, and store that information for future problems. We demonstrate the ability of CLIMB to improve performance in common planning environments compared to baseline methods. We also develop the BlocksWorld++ domain, a simulated environment with an easily usable real counterpart, together with a curriculum of tasks with progressing difficulty for evaluating continual learning. Additional details and demonstrations for this system can be found at https://plan-with-climb.github.io/ .