Only a small remark:
The idea of variable-length lookbehind is very good, but the given problem can be solved even without using lookbehinds at all:

#!/usr/bin/perl

use warnings;
use strict;

my $pat = qr{
             (              # 1: capture the whole substring
               (?:          
                (.)         # a character
                (?!\2\2)    # NOT repeated three times
               ){1,4}       # one to four of such 'good' characters
             ..             # two any characters more; 2+4 = 6
             )
}x;

foreach (qw/AABBCCDD AABBBCCD AAABBCCD AABBCCCD AAABCDE/) {
   print "$1\n" if /$pat/;
}
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outputs

AABBCC
AABB
AABBCC
AABBCC
AABCDE
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