People don't mimic my accent, but I have changed the pronunciation of some words to limit that, namely "water" and "can't". Those are the two that people really used to laugh at.
It is funny though how some people can't place my accent and others, when told how long I've been here, say, "you haven't lost your accent at all!". LOL
I totally get the "do you think you're the first person to point that out?" remark. I once told my husband that sometimes I feel like printing out an FAQ to hand out to people because, when you've been asked the same question 100 times, it's hard to feign interest in responding, though I do try.
How long have you been here?
Where are you from?
Why on earth would you leave LA to live here?
My sister in law lives there, do you know her?
etc.
I don't think he quite believed me but after the fourth or so time, he finally got it. He told me that I still manage to sound convincing and interested in the conversation, so I must be doing something right LOL
He's only been privy to "American slamming" once or twice and he's so protective, I think it bugs him more than me, bless him.
The worst I ever got was, on answering a question about the UK political system, a woman said, "My word! That was such an intelligent response!". Everyone stared at her blankly, so she said, "well, I think we'd all agree that Americans are fundamentally braindead".