The interest of the space industry in Real-Time Operating Systems for achieving stringent real-time requirement is drastically increasing. Among the different available hardware architectures, the solution of RTOS implemented on soft processors embedded in programmable devices is one of the most efficient and flexible solution for the mission deployment. However, radiation-induced failures are a severe concern affecting the reliability of electronic systems in space applications. In this paper, we investigate the impact of radiation-induced architectural faults affecting the reliability of application running on a Xilinx Microblaze embedded soft-processor within FreeRTOS Operating System. We developed a fault model through a proton radiation test, while the effects of the faults are evaluated in terms of Mean Time To Failure and Mean Executions To Failure, by a fault injection campaign using detected fault models. Finally, the occurrence and contribution to the error rate of specific MBUs events based on different shapes and sizes are evaluated through dedicated fault injection campaigns.