I thought maybe it would be helpful to display the HTML dump of each of these, just in case.
This is the HTML for the working LINKS section
<center><table border='1'>
<tr><td colspan="2"><center><b>Adjust link display order</b></center><
+/td></tr>
<form action='process.cgi' method='post'>
<input type='hidden' name='section' value='links'>
<input type='hidden' name='action' value='link_order'>
<input type='hidden' name='orders_list' value='1:2'>
<input type='hidden' name='link_id_list' value='20:21'>
<tr><td>FreeStuff</td>
<td>
1 <input type='radio' name='order_20' value='1' checked>2 <input type=
+'radio' name='order_20' value='2'></td></tr>
<tr><td>Freebies</td>
<td>
1 <input type='radio' name='order_21' value='1'>2 <input type='radio'
+name='order_21' value='2' checked></td></tr>
<tr><td colspan="2"><center><input type='submit'></center>
</table></center>
</form>
And this is the HTML output of the broken referal section
<i>Adjust referrers display order</i></b><br>
<table border='1'>
<form action='process.cgi' method='post'>
<input type='hidden' name='section' value='referrers'>
<input type='hidden' name='action' value='link_order'>
<input type='hidden' name='orders_list' value='1:1:1:1:1:1'>
<input type='hidden' name='link_id_list' value='21:14:16:22:20:19'>
<tr><td>Site A</td>
<td>
1 <input type='radio' name='order_21' value='1' checked>1 <input type=
+'radio' name='order_21' value='1' checked>1 <input type='radio' name=
+'order_21' value='1' checked>1 <input type='radio' name='order_21' va
+lue='1' checked>1 <input type='radio' name='order_21' value='1' check
+ed>1 <input type='radio' name='order_21' value='1' checked></td></tr>
<tr><td>SiteB</td>
<td>
1 <input type='radio' name='order_14' value='1' checked>1 <input type=
+'radio' name='order_14' value='1' checked>1 <input type='radio' name=
+'order_14' value='1' checked>1 <input type='radio' name='order_14' va
+lue='1' checked>1 <input type='radio' name='order_14' value='1' check
+ed>1 <input type='radio' name='order_14' value='1' checked></td></tr>
<tr><td>Site C</td>
<td>
1 <input type='radio' name='order_16' value='1' checked>1 <input type=
+'radio' name='order_16' value='1' checked>1 <input type='radio' name=
+'order_16' value='1' checked>1 <input type='radio' name='order_16' va
+lue='1' checked>1 <input type='radio' name='order_16' value='1' check
+ed>1 <input type='radio' name='order_16' value='1' checked></td></tr>
<tr><td>Site D</td>
<td>
1 <input type='radio' name='order_22' value='1' checked>1 <input type=
+'radio' name='order_22' value='1' checked>1 <input type='radio' name=
+'order_22' value='1' checked>1 <input type='radio' name='order_22' va
+lue='1' checked>1 <input type='radio' name='order_22' value='1' check
+ed>1 <input type='radio' name='order_22' value='1' checked></td></tr>
<tr><td>Site E</td>
<td>
1 <input type='radio' name='order_20' value='1' checked>1 <input type=
+'radio' name='order_20' value='1' checked>1 <input type='radio' name=
+'order_20' value='1' checked>1 <input type='radio' name='order_20' va
+lue='1' checked>1 <input type='radio' name='order_20' value='1' check
+ed>1 <input type='radio' name='order_20' value='1' checked></td></tr>
<tr><td>Site F</td>
<td>
1 <input type='radio' name='order_19' value='1' checked>1 <input type=
+'radio' name='order_19' value='1' checked>1 <input type='radio' name=
+'order_19' value='1' checked>1 <input type='radio' name='order_19' va
+lue='1' checked>1 <input type='radio' name='order_19' value='1' check
+ed>1 <input type='radio' name='order_19' value='1' checked></td></tr>
</table>
<input type='submit'>
</form></center>