I have not benchmarked this, but it is probably faster than your current version. HTH

use warnings;
use strict;

while (<DATA>) {
  chomp;
  print "$_ -> ";

  my $len = length;

  if ( s/(\w)\1{2,}\Z/$1$1/ ) {
    $len -= length;
    print "$len -> $_";
  }

  print "\n"; 
}

__DATA__
ACTGCTAGGGGGGG
TCAGCTAGCNA
ACTGSCGACAAAA
GTCTGAGTTATTT
[download]

Update: davido encouraged me to present my alternative version. I converted the original array based variation into a string based one, hoping (not measured) for better speed. So, in the sense of TIMTOWTDI:

use strict;
use warnings;

my $in = shift || 'GATATTTTTTT';

$_       = $in;
my $last = substr $_, -1;

if ( length > 2  and  substr($_, -2, 1) eq $last ) {
   chop while substr($_, -1) eq $last;
   $_ .= $last . $last;
}

print "in : $in\n";
print "out: $_\n";
[download]