Keeping Our Promise Act This bill authorizes issuing visas to certain individuals who were previously refused a diversity immigrant visa or admission into the United States because of certain executive orders or the COVID-19 public health emergency. (Diversity immigrant visas are available to eligible immigrants from countries with relatively low rates of immigration to the United States.) Specifically, this bill applies to individuals who were refused such a visa solely due to certain executive orders from 2017 to 2020, including orders which suspended the entry of individuals from certain countries. The bill also applies to diversity visa applicants who, because of the COVID-19 emergency, were (1) unable to receive a visa interview despite requesting one, or (2) unable to be admitted into the United States despite being approved for a visa. The Department of State must notify each individual covered under this bill of the individual's visa eligibility. To retain eligibility, an individual must respond to the State Department's notice within one year of the notice. An individual may also lose eligibility if the State Department determines that the applicant fails to meet certain requirements. The bill also relaxes certain annual numerical limits for individuals obtaining a visa under this bill. An individual who was a child when initially selected for a visa shall be treated as a child for the purposes of a visa application under this bill.