>perl script.pl
Match: GNN at 7
Match: GNN at 7
Match: GNN at 7
Match: GNN at 7
Match: GNN at 7
Match: GNN at 7
Match: GNN at 7
Match: GNN at 7
...
[download]

It seems my Perl's tr/// clears pos for all strings. Workaround:

use strict;
use warnings;

my %seq;
my $k = 0;

$seq{$k} = 'xxxxxxxGNNNxxxxxxxNNNGYGYxxxxxxxGYGYNNNxxxxxxxNNNGNNNxxxxx
+xx';

# break up three character repeats, inserting spaces
while ($seq{$k} =~ s/([QGYN])\1\1/$1$1 $1$1/g) { }

while ($seq{$k} =~ m/([QGYN]{3,5})/g) {
   my $saved_pos = pos($seq{$k});
   printf("Match: %s at %d\n", 
      $1,
      pos($seq{$k}) - length($1)-2*(substr($seq{$k}, 0, pos($seq{$k}))
+ =~ tr/ / /),
   );
   pos($seq{$k}) = $saved_pos;
}
[download]

Finally, a solution that works!