Intelligent and reliable task planning is a core capability for generalized robotics, which requires 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 feedback from execution to guide the construction of domain models. 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 developed the BlocksWorld++ domain, a simulated environment with an easily usable real counterpart, together with a curriculum of tasks with progressing difficulty to evaluate continual learning. Code and additional details for this system can be found at https://plan-with-climb.github.io/.