I think you need to first create an instance of JLogger using JLog::addLogger. If you look at how the logging is done in core, you will see something like the following:
$options['format'] = '{DATE}\t{TIME}\t{LEVEL}\t{CODE}\t{MESSAGE}';
$options['text_file'] = 'joomla_update.php';
JLog::addLogger($options, JLog::INFO, array('Update', 'databasequery', 'jerror'));
JLog::add(JText::_('COM_JOOMLAUPDATE_UPDATE_LOG_DELETE_FILES'), JLog::INFO, 'Update');
You only need one instance of the logger and then you can use JLog:add() as many times as you need.
Hope that helps. Mark