Moved the query from the loop into a sub query and then optimized a little.

chapter.php

<?php
public function getSubmits()
  {
		$cid = JFactory::getApplication()->input->getInt('cid');
		
		$db = $this->getDbo();
		$query = $db->getQuery(true);	
		
		$query->select('a.*, i.username');
		$query->select('(SELECT SUM(v.vote) FROM #__rootflick_vote AS v WHERE v.sub_id = a.id) AS vote');
		$query->from('#__rootflick_submissions as a');
		$query->leftJoin('#__users as i ON (a.user_id = i.id)');
		$query->where('chapter_id='.$cid . ' and winner = 0');

		return $db->setQuery($query)->loadObjectList();
	}
?>