Well, when I do what you've done, the tags remain, but when I switch the editor to Visual mode and back to HTML mode, they vanish and the resulting web page goes back to being invalid.
Deactivation of plugins makes no difference. It's the WordPress editor.
Just in case, I checked "WordPress should correct invalidly nested XHTML automatically" and tested again. No luck.
I believe what happens is that end-of-lines before the closing TD tag is removed by the editor and when the page is prepared for the browser, it is left as is. If I insert two end-of-lines before the closing TD tag in HTML view and save, the page is coded correctly!
Here's the table code, as it appears in HTML view within the WordPress editor, if anyone wants to test:
<tbody>
<tr>
<td>
<h3><a href="http://www.themotivationalspeaker.biz/index.php/motivational-presentations/cultural-awareness-and-diversity/">Cultural Awareness and Diversity</a></h3>
<a href="http://www.themotivationalspeaker.biz/index.php/motivational-presentations/cultural-awareness-and-diversity/"><img title="diversity" src="http://www.themotivationalspeaker.biz/wp-content/uploads/2009/03/diversity2.jpg" alt="diversity" /></a>A range of experiences and interactive presentations about acceptance, culture, immigration, multilingualism, multiculturalism and social justice.</td>
<td>
<h3><a href="http://www.themotivationalspeaker.biz/index.php/motivational-presentations/communication-and-relationships/">Communication and Relationships</a></h3>
<a href="http://www.themotivationalspeaker.biz/index.php/motivational-presentations/communication-and-relationships/"><img title="diversity" src="http://www.themotivationalspeaker.biz/wp-content/uploads/2009/04/family3-300x231.jpg" alt="diversity" /></a>Simple, accessible and practical workshops and presentations about communication, relationships, teamwork, love, friendship, parenting and just how to get along with others.</td>
</tr>
</tbody>
</table>