AI coding agents are now submitting pull requests (PRs) to software projects, acting not just as assistants but as autonomous contributors. As these agentic contributions are rapidly increasing across real repositories, little is known about how they behave in practice and why many of them fail to be merged. In this paper, we conduct a large-scale study of 33k agent-authored PRs made by five coding agents across GitHub. (RQ1) We first quantitatively characterize merged and not-merged PRs along four broad dimensions: 1) merge outcomes across task types, 2) code changes, 3) CI build results, and 4) review dynamics. We observe that tasks related to documentation, CI, and build update achieve the highest merge success, whereas performance and bug-fix tasks perform the worst. Not-merged PRs tend to involve larger code changes, touch more files, and often do not pass the project's CI/CD pipeline validation. (RQ2) To further investigate why some agentic PRs are not merged, we qualitatively analyze 600 PRs to derive a hierarchical taxonomy of rejection patterns. This analysis complements the quantitative findings in RQ1 by uncovering rejection reasons not captured by quantitative metrics, including lack of meaningful reviewer engagement, duplicate PRs, unwanted feature implementations, and agent misalignment. Together, our findings highlight key socio-technical and human-AI collaboration factors that are critical to improving the success of future agentic workflows.