https://getpocket.com/explore/item/when-did-americans-lose-their-british-accents?utm_source=pocket-newtab
This is kind of like asking when humans lost their tails. Americans never "lost" their British accent; both contemporary British and American accents evolved from precolonial British accents that no longer exist today. Also, there is obviously much more to an accent than whether or not it is rhotic, and the rhotic/non-rhotic feature of an accent can evolve independently of the same feature in another accent. Like how bats and birds have analogous wings that were not inherited from a common ancestor.
A more interesting question to me would be how Canadian English developed. Some of its distinctive characteristics were, I understand, deliberately encouraged by the government in an effort to fight off "Americanization" yet Canadians do not speak "public school English" any more than we do in the States.
Interesting to read British accent. Britian is an island with multiple countries and multiple languages. Multiple dialects and accents occur all over the island. I would love to visit Tangier Island on the Eastern Shore of Virginia. The (American) English language spoken there has intrigued linguistics scholars for some time.
American English has accents and even dialects, like Southern English and very different accent of English in NY. Not only as usual process words from other languages entered but also accents that inn country of migrants its expected even more. I watched an interview with Bill Clinton with long vowels and relaxed pronunciation. Also Floridan's accent, caint - can't (I caint do that.) fitt'in - fixing to, about to (I'm fitt'in to buy one.) fitty - fifty (Can I borrow fitty cents?) i'moan - I am going to (I'moan go to that game.) Ebonics is like a different dialect, and strange English in a hasidic neighborhood.