If you really mean that "AAaaa" should be lower-cased, but not "ABaaa", this will work:

$string =~ s/(([A-Z])\2+)/lc $1/eg;
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On the other hand, if you want to also lower-case "ABaaa", this will do it:

$string =~ s/([A-Z]{2,})/lc $1/eg;
[download]

TIMTOWTDI. I provided these for the fun of using the {2,} style quantifier.

By the way, if there's any possibility that you'll be working with non-standard-ASCII character sets (ie, Unicode, etc.) all of the methods so far could break down. It's always a little risky to assume that the entire set of upper-case characters fall within the range 'A'..'Z'. In other words, none of the solutions presented so far are portable to a broad range of languages and text encoding schemes. If that is possibly an issue, look into the POSIX extensions for regexps, and consider using a named character class to represent upper case characters.

For completeness, here are the Unicode-compliant, POSIX versions of the above regexes:

$string =~ s/(([:upper:])\2+)/lc $1/eg;
$string =~ s/([:upper:]{2,})/lc $1/eg;
[download]