Unikałbym wykonywania zapytania dla każdego wpisu.
if(is_array($EMailArr)){
$sql = "INSERT INTO email_list (R_ID, EMAIL, NAME) values ";
$valuesArr = array();
foreach($EMailArr as $row){
$R_ID = (int) $row['R_ID'];
$email = mysql_real_escape_string( $row['email'] );
$name = mysql_real_escape_string( $row['name'] );
$valuesArr[] = "('$R_ID', '$email', '$name')";
}
$sql .= implode(',', $valuesArr);
mysql_query($sql) or exit(mysql_error());
}