I was in a psychology study a while back at my uni, which was specifically for native English speakers who weren't born in the UK. I quite happily signed up (£20 voucher!), only to be told after an hour of reading off of flashcards that they couldn't use my results.
Apparently, while many people retain their non-British pronunciation of words, after a certain amount of time (varying between people), almost everyone unconsciously adopts the rhythm and stresses of speaking common in their environment. It's why people in the UK think that you sound American, and you think that you've kept your accent, but when you go back to the US people say that you sound different. So what we end up with is some sort of mutant accent with American pronunciation and British rhythm.
One prominent example is how pitch differs at the end of a question - with a native US accent the pitch goes up quite a lot, while in a British accent it's usually either monotone or only a very slight rise (and sometimes even goes down slightly).
Of course slang is another, more obvious thing. It's no good to speak with an American accent if you're unintentionally using words and phrases that no one back home understands.
