IE assumes that the clicking of a link heralds a new navigation where the current page contents will be replaced. As part of the process for perparing for that it halts the code that animates the GIFs. I doubt there is anything you can do about it (unless you aren't actually navigating in which case use return false in the onclick event).

The accepted solution did not work for me.
After some more research I came across this workaround, and it actually does work.
Here is the gist of it:
<script>
function showProgress() {
var pb = document.getElementById("progressBar");
pb.innerHTML = '<img src="./progress-bar.gif" width="200" height ="40"/>';
pb.style.display = '';
}
</script>

and in your html:
<input type="submit" value="Submit" onclick="showProgress()" />
<div id="progressBar" style="display: none;"><img src="./progress-bar.gif" width="200" height ="40"/></div>

So when the form is submitted the img tag is inserted which for some reason it is not effected by the ie animation issues.
Tested in Firefox, ie6, ie7 and ie8.

IE assumes that the clicking of a link heralds a new navigation where the current page contents will be replaced. As part of the process for perparing for that it halts the code that animates the GIFs. I doubt there is anything you can do about it (unless you aren't actually navigating in which case use return false in the onclick event).

I tried the solution given by AnthonyWJones above by adding -

return false;

at the end of the script in the clicked link and it worked. Thanks!