Using a simple substitution with look behind and look ahead seems to fit the bill:

use strict;
use warnings;

my $str = 'XAXAAAAXXXXXXXAAXXXXXAXXXXAAAAX';
my $before = $str;

$str =~ s/(?<=A)(X+)(?=A)/'a' x length $1/ge;
print "$before\n";
print "$str\n";
[download]

Prints:

XAXAAAAXXXXXXXAAXXXXXAXXXXAAAAX
XAaAAAAaaaaaaaAAaaaaaAaaaaAAAAX
[download]

with lower case 'a' used to make the substitutions clear.