not quite sure what your trying to accomplish with this, but both loops are using the same recordset try changing it to:
<?php do { ?> <p><?php echo $row_rsMin['Title']; ?></p>
<?php do { ?>
<p><?php echo $row_rsSubmin['Title']; ?></p>
<?php } while ($row_rsSubmin = mysql_fetch_assoc($rsSubmin)); ?>
<?php } while ($row_rsMin = mysql_fetch_assoc($rsMin)); ?>