We explore the mental health of elderly in relation to social determinants of health (SDOH) during the COVID pandemic. Factors such as physical isolation and social disconnectedness, resulting from interventions such as home isolation and restricted visits to nursing homes, are considered as potential contributors to the decline in mental health. By leveraging data from the All of Us Research Program, we explore the relationship between mental health outcomes and SDOH among a large cohort of elderly participants. Male gender and reporting being African American appear to be associated with relatively better mental health outcomes, whereas being divorced, separated, or widowed is linked to poorer mental health. Income and education demonstrate inconsistent effects on mental health outcomes. The deep neural network models outperform regression models in the same outcomes, by modeling more complex relationships between variables. Predictive performance remains modest for COVID-related anxiety and general well-being.