Pregnancy Loss Mental Health Research Act of 2021 This bill expands research and related activities that address mental health complications following a pregnancy loss (i.e., miscarriage, stillbirth, or abortion). Specifically, the National Institutes of Health and the National Institute of Mental Health (NIMH) must expand and intensify research on mental health complications following pregnancy loss. In particular, NIMH must conduct a longitudinal study to determine the prevalence and other information about such mental health complications. Additionally, the Department of Health and Human Services must award grants to health providers, state or local governments, or other appropriate nonprofits to deliver services to individuals with mental health conditions following a pregnancy loss. Funding made available under this bill may not be provided to an entity (or an entity's affiliate, subsidiary, successor, or clinic) that performs abortions other than in the case of a pregnancy (1) that is the result of rape or incest; or (2) when the life of the woman is in danger due to a physical disorder, injury, or illness.