There's a small bug with unpublishing polls from front-end. See site/models/polls.php on line 2081:

$query = 'UPDATE #__jcp_polls SET published='.$this->_db->getEscaped($state).' WHERE id='.$this->_db->getEscaped($cid);

This line was the problem with SQL query error. So I changed it to this one:

$query = "UPDATE #__jcp_polls SET published = '".$state."' WHERE id = '".$cid."'";

And now everything works good. Please, check this.