Language models (LMs) are increasingly used to build agents that can act autonomously to achieve goals. During this automatic process, agents need to take a series of actions, some of which might lead to severe consequences if incorrect actions are taken. Therefore, such agents must sometimes defer-refusing to act when their confidence is insufficient-to avoid the potential cost of incorrect actions. Because the severity of consequences varies across applications, the tendency to defer should also vary: in low-risk settings agents should answer more freely, while in high-risk settings their decisions should be more conservative. We study this "answer-or-defer" problem with an evaluation framework that systematically varies human-specified risk structures-rewards and penalties for correct answers, incorrect answers, and refusals $(r_{\mathrm{cor}},r_{\mathrm{inc}}, r_{\mathrm{ref}})$-while keeping tasks fixed. This design evaluates LMs' risk-aware decision policies by measuring their ability to maximize expected reward. Across multiple datasets and models, we identify flaws in their decision policies: LMs tend to over-answer in high-risk settings and over-defer in low-risk settings. After analyzing the potential cause of such flaws, we find that a simple skill-decomposition method, which isolates the independent skills required for answer-or-defer decision making, can consistently improve LMs' decision policies. Our results highlight the current limitations of LMs in risk-conditioned decision making and provide practical guidance for deploying more reliable LM-based agents across applications of varying risk levels.