Lets cycle back to our friends at Factcheck and FTS:
Fight the Smears: The Truth About Barack
"When Barack Obama Jr. was born on Aug. 4,1961, in Honolulu, Kenya was a British colony, still part of the United Kingdom's dwindling empire. As a Kenyan native, Barack Obama Sr. was a British subject whose citizenship status was governed by The British Nationality Act of 1948. That same act governed the status of Obama Sr.'s children:
Read that last sentence again" That same act governed the status of Obama Sr.'s children." That means he was born a dual citizen. A dual citizen is not a natural born citizen.
British Nationality Act of 1948 (Part II, Section 5): Subject to the provisions of this section, a person born after the commencement of this Act shall be a citizen of the United Kingdom and Colonies by descent if his father is a citizen of the United Kingdom and Colonies at the time of the birth."
British Nationality Act 1948
So Obama has British Citizenship at the time of birth, that is a given. Did he gain citizenship to Kenya? Yes - via Chapter VI, Section 87(2):
"(2) Every person who, having been born outside Kenya, is on
11th December, 1963 a citizen of the United Kingdom and Colonies or
a British protected person shall, if his father becomes, or would but for
his death have become, a citizen of Kenya by virtue of subsection (1),
become a citizen of Kenya on 12th December, 1963."
But did becoming a Kenyan Citizen terminate British Citizenship? We look into the Kenyan Constitution and find - NO, it did not. See Chapter VI, Section 95(1):
"95. (1) Every person who, under this Constitution or an Act of
Parliament, is a citizen of Kenya or who, under any law for the time
being in force in a country to which this section applies, is a citizen
of that country shall, by virtue of that citizenship, have the status of a
Commonwealth citizen."
So Obama has never renounced his British Citizenship gained at birth. He never 'automatically' lost it, even when Kenya became independent.
All U.S.presidents since the grandfather clause ran out were born to two U.S. citizens with the exception of Chester Arthur who was found out later not eligible.