This is a confirmed issue in IE (google and you will see many complaints). This SO post recommends using a combination of deleting and re-adding or cloning and re-adding objects every time you show / hide tabs.
An alternative approach, since it seems that you are using exclusively embedded YouTube videos, you should use the YouTube JavaScript Player API and stop the video every time the tab is displayed and / or hidden.
Updated to include an example:
JS API YouTube . SWFObject, , , , , . -, SWFObject , :
<p><a id="showhide" href="#show">show/hide with YT API pause</a></p>
<div id="tab">
<object id="video1" width="640" height="385" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000">
<param name="movie" value="http://www.youtube.com/v/sUO4bnWtlnE&hl=en_US&fs=1&enablejsapi=1"></param>
<param name="allowscriptaccess" value="always"></param>
<embed src="http://www.youtube.com/v/sUO4bnWtlnE&hl=en_US&fs=1&enablejsapi=1" type="application/x-shockwave-flash" allowscriptaccess="always" width="640" height="385"></embed>
</object>
</div>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.2/jquery.min.js"></script>
<script>
(function () {
var tab = $('#tab'),
video1 = $('#video1')[0];
$('#showhide').click(function (evt) {
if (video1.pauseVideo) video1.pauseVideo();
tab.toggle();
return false;
});
})();
</script>
jsFiddle .