The effective implementation of Open and Distance e-Learning (ODeL) in Nigeria requires reliable power supply. This is because the computing systems that are used rely on electricity; as a result, persistent power outages will significantly impede its success. This study set out to investigate how unstable electricity supply affects the functionality and sustainability of ODeL infrastructure across selected Nigerian institutions. In order to achieve this, we employed a mixed-methods approach; this includes surveys, interviews, and case studies. The research work assesses the state of energy infrastructure and its implications for online education delivery. Our findings revealed that frequent disruptions to power supply limit access to virtual classrooms, digital resources, and learner engagement, which has a negative effect on students in rural and low-income communities. The study identifies other barriers to Open and Distance learning to include infrastructural deficits and inadequate energy policies; it also proposes practical and scalable solutions such as the integration of renewable energy sources like solar and wind power, the deployment of energy-efficient technologies, and the adoption of hybrid learning frameworks to enhance resilience. Furthermore, this research work emphasizes the importance of policy reform and strategic public-private partnerships in addressing systemic energy challenges. Finally, the output of this research reveals the need to strengthen energy infrastructure as a prerequisite for inclusive and equitable ODeL in Nigeria, so as to foster resilient educational systems which will be capable of withstanding infrastructural limitations and expanding access to quality learning opportunities.