Looks like a good place for the flip-flop .. operator. So your code would look like this (untested).

while  (my $token = $stream->get_token) {
  if (($token->[0] eq 'C' and 
       $token->[1] eq '<!-- InstanceBeginEditable name="article" -->')
      ..
       ($token->[0] eq 'C' and $token->[1] eq '<!-- InstanceEnd -->'))
+{
    print $token->[1];
  }
}
[download]

Should work (although it might have off-by-one problems, and the style might be confusing). Alternately, you could use a separate variable to keep track of your state.

my $parsing=undef;
while  (my $token = $stream->get_token) {
  if ($token->[0] eq 'C' and 
      $token->[1] eq '<!-- InstanceBeginEditable name="article" -->'){
    $parsing=1;
  } elsif ($token->[0] eq 'C' and 
           $token->[1] eq '<!-- InstanceEnd -->') {
    $parsing=undef;
  } elsif ($parsing) {
    print $token->[1];
  }
}
[download]