Existing dynamic vulnerability patching techniques are not well-suited for embedded devices, especially mission-critical ones such as medical equipment, as they have limited computational power and memory but uninterrupted service requirements. Those devices often lack sufficient idle memory for dynamic patching, and the diverse architectures of embedded systems further complicate the creation of patch triggers that are compatible across various system kernels and hardware platforms. To address these challenges, we propose a hot patching framework called StackPatch that facilitates patch development based on stack frame reconstruction. StackPatch introduces different triggering strategies to update programs stored in memory units. We leverage the exception-handling mechanisms commonly available in embedded processors to enhance StackPatch's adaptability across different processor architectures for control flow redirection. We evaluated StackPatch on embedded devices featuring three major microcontroller (MCU) architectures: ARM, RISC-V, and Xtensa. In the experiments, we used StackPatch to successfully fix 102 publicly disclosed vulnerabilities in real-time operating systems (RTOS). We applied patching to medical devices, soft programmable logic controllers (PLCs), and network services, with StackPatch consistently completing each vulnerability remediation in less than 260 MCU clock cycles.