You could use cookie, session for this or other storage method if your visitor/user is online/logged in on the page.
If going for session/cookie you would do:
<?php
while($result_row=mysql_fetch_array($result)){
if ( $_COOKIE['MY_COOKIE'] == $result_row[importance_level_id )
{
echo "<option SELECTED=\"SELECTED\" value=$result_row[importance_level_id]>$result_row[importance_level]</option>";
}
else
{
echo "<option value=$result_row[importance_level_id]>$result_row[importance_level]</option>";
}
?>
make sure you set your cookie/session when user post the form.