Reduced test:

  $file = __DIR__ . '/input_dummy.txt';
  $data = str_repeat( '.', 8189 ) . 'MMMM';
  file_put_contents( $file, $data );
  $fh = fopen( $file, "rb" );
  $delimiter = "MM";

  stream_get_line($fh, 4096, $delimiter);
  stream_get_line($fh, 4096, $delimiter);
  if ($delimiter === stream_get_line($fh, 4096, $delimiter)) {
    echo "BROKEN";
  } else {
    echo "OK";
  }
  fclose($fh);
  unlink($file);

The amount of dots seems to be related to the used buffer length:

(<number-of-dots> + 3) % (<buffer-length> x 2) == 0

The length of the delimiter also seems to play a role, but I'm not sure what 
that would be.

Added a patch that will apply to 5.4.4

Thanks, I'll commit this tomorrow.

As to your other comment on the list about the bool(false) return instead of an empty string for an empty file, that was a bug fix. A return of "" would indicate an empty line. The result is now corect:

$ php -r '$fd = fopen("php://temp", "r+"); var_dump(stream_get_line($fd, 10, "MM"));'
bool(false)
$ php -r '$fd = fopen("php://temp", "r+"); fwrite($fd, "MM"); rewind($fd); var_dump(stream_get_line($fd, 10, "MM"), stream_get_line($fd, 10, "MM"));
string(0) ""
bool(false)

Is it tomorrow yet? :)

Yes, this has already been committed. See the "All" tab in the "History" section of this bug report page and you'll find a link to the revision.