Environmental guidelines in the automotive industry greatly emphasize the recycling, remanufacturing, and recovering of end-of-life vehicles (ELVs). Given the principle of extended producer responsibility, developing an effective reverse logistics network is the most significant digit ahead of the industry. However, initial attempts addressing the reverse logistics network design (RLND) problem were short-sighted, focusing on cost minimization. Undoubtedly, the whole concept of recycling was founded on the pillars of sustainability. Accordingly, reverse logistics network design must be motivated by long-term environmental and societal benefits. This fact has become even more prominent in the current pandemic environment as COVID-19 has added serious uncertainties and risks to the supply chain processes. This paper reiterates the essence of sustainability goals and proposes a multi-objective fuzzy mathematical model to RLND problem for ELVs under such a fragile and fuzzy environment. The coverage of the proposed model is to optimally determine the locations and numbers of the facilities and the flows among them concerning environmental, social, and economic aspects. Hence, the model aims to reach a robust compromise solution that leads to a resilient network design. A real case study on the ELV market in Istanbul/Turkey proves the merit of the developed model.