Redcoats' revenge

What if, on September 11, 1814, the United States had lost the close-run battle that Winston Churchill called the "most decisive" of the War of 1812? With a victory at Plattsburgh, would the British have eventually been able to regain control of their former colonies? Only one fleeting moment on Lake Champlain might have been needed to forever alter the young country's history and return it to the grip of King George III.