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I think no one can actually "loose" their accents, you can turn it on and off as you wish, but sometimes, you will mix between two without you knowing.
Speaking for myself, i am an american at birth and move to Sydney about 10 years ago, all my friend in Australia told me i still speak american, but all my friend in the states told me i speak australian. You be the judge.
At this point, i should point out i was a language threapist, my job is to help people loose their accents (Indian, Chinese, European, African, etc) as far as i know and seen, none of them can migrate from one accent to another, totally.

As has been mentioned, he rarely speaks in an Australian accent now. He deliberately took lessons on American dialect in the late 70's so that he could act in Hollywood productions so you rarely hear it at all in his work since then. However, it is quite noticable on his early records (including the 1972 album BEGINNINGS) and on the 1974 children's cartoon MISSION MAGIC which is on DVD.

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i saw him yesterday and it was pretty much not there, he's had about 30 years of practice, and kind of once they make an aussie loose his accent, they make him loose it for everything
dominic procell..(prison break) had to loose it, and he won't use it on talk shows, or anything like that, the same goes for julian macmahon..(sp) nip/tuck, although he had trouble getting rid of it at first, you'll never hear any of them using it, even on talk shows, there are other aussie actors that are the same
even ingo radamaker..(jax) GH.doesn't have that much of a one anymore..it's kind of sad, because i just love an aussie accent
susan

Heard him talking last night and did not hear his accent, except for a couple of seconds when he teased someone in the audience with a British accent and he started to talk with HIS accent (just a few words).

It's natural to pick up the local way of talking when you move to a different place. I had an elderly co-worker who was born and raised in England, and spent his adult life in America. He still has an English accent (at least to me), but some words he uses come out sounding "American." He told me once that whenever he travels back to England, people there think he sounds more like an American.
(insert cool-sounding random quote here)

Actually for the most part his accent is gone. It did pop out again when he did a short tour in Austrailia this past summer. But you can hear certain words that have a twinge of an Aussie accent.
Rick had worked with a dialect coach to help him lose it early on..when he was getting into acting.
I have met him 4 times now, and only hear it on certain type of words. But if you didn't know he was from Austrailia..you probably wouldn't even notice.
Anywayoff to my Rick show in Tacoma WA..Nov. 3

Yes he does I have been to a few of his concerts and have meet him too and he still has his accent (it comes and goes) it's beautiful.