Newbie Q: Populating DT after pageload kills it

Hi, I have this page that loads a DT table when user hits the "Demarer" button.
See: http://www.oreillegauche.com/MRKT/MonitorEmailsDT.php

This fires js XMLHttpRequest() to a PHP scripts that echoes <tr><td> inside the <tbody> tag. It works but as soon as I try to use "search" or order columns, the data disappears and the table goes empty.

Is there a REFRESH function or is it just not the way to do it?
I chose this method over AJAX and server-side because I have very few data and I'm using different CSS color decoration depending on data values (past dates are red, futur dates are green).

THANKS

See HTML code below (I stripped <tfoot> for clarity) :

                <table id="myTable" class="display" cellspacing="0" width="100%">
                   <thead>
                        <tr>
                            <th>ID</th>
                            <th>Prénom</th>
                            <th>Nom</th>
                            <th>Adresse courriel</th>
                            <th>Envoi prévu le</th>
                        </tr>
                    </thead>

                    <tbody id="ToSendList">
                        <!-- TABLE DATA HERE-->
                    </tbody>
                </table>

See js code fired by the "Demarer" button:

var xmlhttp = new XMLHttpRequest();
xmlhttp.onreadystatechange = function() {
if (this.readyState == 4 && this.status == 200) {
document.getElementById("ToSendList").innerHTML = this.responseText;
}
};
xmlhttp.open("GET", "GetEmailListfoDT.php", true);
xmlhttp.send();