Deceased donor kidney allocation is a challenging sequential decision making problem constrained by the limited time that the kidney is medically viable. The decision made at each time point is a tradeoff between preserving equity (i.e., to offer the kidney to the next person on the waiting list) and seeking efficiency (i.e., to expedite to a more accepting patient lower down on the waiting list to avoid discard). Under the current allocation system, organ procurement organizations (OPOs) make ad-hoc decisions on when to prioritize efficiency over equity, leading to uneven treatment for patients skipped on the waitlist. We develop models to predict whether a donor will be hard-to-place based on the initial medical context of this sequential decision process, achieving a balanced accuracy of 80.2%. We improve balanced accuracy to 94.0% by adjusting predictions based on the sequentially updated medical contexts, that is, information accumulated during a kidney's match run. Our model can inform OPOs on whether to expedite a kidney based on their current context. We discuss associated implementation challenges, including those related to equity.