Maybe not during the 20th century, but the Supreme Court suggested it was possible in the Wong Kim Ark decision in 1898:
and neither he nor his parents acting for him ever renounced his allegiance to the United States ...
This same statement is in the decision twice:
that said Wong Kim Ark has not, either by himself or his parents acting [p705] for him, ever renounced his allegiance to the United States,Even in the rare case of an American child adopted by foreign parents, where the birth certificate is updated to reflect the foreign parents, U.S. citizenship is maintained.
Except that the State Department can't guarantee the protection of U.S. citizenship when an adoption is in a country that doesn't recognize dual citizenship. But, we don't know that Obama even had U.S. citizenship prior to being adopted, thus there may have been no U.S. citizenship to maintain.
And the Supreme Court in Perkins v. Elg (1939) basically said that it was impossible for someone other than the person themselves to surrender their citizenship.
Furthermore, the United States State Department basically says that while it is theoretically possible, people under 16 are presumed to not have the maturity for it to happen.