You can disable file upload button after upload complete using javascript
<ajaxToolkit:AsyncFileUpload
OnClientUploadError="uploadError" OnClientUploadComplete="uploadComplete"
runat="server" ID="AsyncFileUpload1" />
<script type="text/javascript">
function uploadError(sender, args) {
}
function uploadComplete(sender, args) {
document.getElementById("yourButtonID").disabled = true;
}
</script>
Hope this helps