If I'm understanding you correctly:

#!/usr/bin/perl
my @seqs=qw(AAAA  ABAB CCC DDDDDDD EEEEFFF);
foreach my $seq (@seqs) {
    if($seq =~m/^(\w)\1{2,6}$/) {
        print "$seq: REPEATED\n";
    } else {
        print "$seq: NOT REPEATED\n";
    }
}

Outputs:
AAAA: REPEATED
ABAB: NOT REPEATED
CCC: REPEATED
DDDDDDD: REPEATED
EEEEFFF: NOT REPEATED
[download]

But that would only match things like AAAA versus things like AAAAABBB. Not sure exactly what behavior you're looking for.

Edit: The magic here is backreferences and capture groups. See this bit in the perlre docs.