The dynamic of the Linux kernel heap layout significantly impacts the reliability of kernel heap exploits, making exploitability assessment challenging. Though techniques have been proposed to stabilize exploits in the past, little scientific research has been conducted to evaluate their effectiveness and explore their working conditions. In this paper, we present a systematic study of the kernel heap exploit reliability problem. We first interview kernel security experts, gathering commonly adopted exploitation stabilization techniques and expert opinions about these techniques. We then evaluate these stabilization techniques on 17 real-world kernel heap exploits. The results indicate that many kernel security experts have incorrect opinions on exploitation stabilization techniques. To help the security community better understand exploitation stabilization, we inspect our experiment results and design a generic kernel heap exploit model. We use the proposed exploit model to interpret the exploitation unreliability issue and analyze why stabilization techniques succeed or fail. We also leverage the model to propose a new exploitation technique. Our experiment indicates that the new stabilization technique improves Linux kernel exploit reliability by 14.87% on average. Combining this newly proposed technique with existing stabilization approaches produces a composite stabilization method that achieves a 135.53% exploitation reliability improvement on average, outperforming exploit stabilization by professional security researchers by 67.86%.