<p>This research, grounded in the theory of sustainable family businesses (SFBT), leverages the unprecedented context of the COVID-19 crisis to explore the mediating role of adaptive capacity in the relationship between organizational sensitivity—comprising stakeholder sensitivity and process sensitivity to COVID-19—and recovery from the pandemic. A structured questionnaire was administered to 212 small family businesses in Mexico. The collected data were analyzed using exploratory factor analysis (EFA) to determine variable composition, followed by correlation and regression analyses to investigate interrelationships. The findings demonstrate that adaptive capacity mediates the relationship between sensitivity in operational processes to COVID-19 and post-pandemic business recovery. These results offer valuable insights for the development of organizational management strategies and public policies tailored to enhance the resource accumulation and investment capacity of family businesses. Plain English Summary. Small family businesses are susceptible to the crises but also flexible in developing the capacity to adapt and recover. This research shows that the company is sensitive to the illness and death of its stakeholders and the organizational processes. Faced with these challenges, the capacity to adapt is developed to recover the business. Although the capacity for adaptation functions as a mediator between the sensitivity of organizational processes, this does not happen with the sensitivity of the stakeholders. The main implication of this study is that recognizing the sensitivity of an organization allows for generating better adaptation options in the tension between the accumulation and investment of resources, thereby achieving better recovery levels. Addressing these aspects will make organizations more resilient to crisis by generating business and public policy actions in this regard.</p>