Bootstrap alert won't close after initial appearance

This is a very difficult problem to explain and demo, basically I am using a mixture of PHP, Smarty, Ajax and Bootstrap.

I have a smarty template with an Ajax form in it (this works), a PHP backend which adds the form details into a database (this also works), on success or failure an alert is shown, this alert is from the Bootstrap CSS, it is written to the page as follows.

$('form').append('<div class="alert alert-success alert-dismissible" role="alert">' + data.message + '<a href="#" class="close" data-dismiss="alert" aria-label="close">&times;</a></div>');

The alert does display in the page, and the alert does close! However, for example if I or the user should want to use the form again for example, to say add another record to the database, the alert does show, but this time it never closes! So if I add another 10 records and click the submit button after each one as normal I have 10 alert boxes under the form that never close.

<script type="text/javascript">
    window.setTimeout(function() {
        $(".alert").fadeTo(1000, 0).slideUp(1000, function() {
            $(this).hide();
        });
    }, 5000);
</script>

Does anyone have an idea as to what I could do instead that would work perhaps?

The below code closes the alert, but there is some inconsistency as to when the alert closes.

$(document).ready(function() {
    $('form').submit(function(event) {

        // snip

        var alertTimer1 = window.setInterval(function() {
            if (typeof alertTimer2 === 'undefined') {
                var alertTimer2 = window.setTimeout(function() {
                    $('#alert').find('.alert').fadeTo(1000, 0).slideUp(1000, function() {
                        $(this).remove();

                        window.clearInterval(alertTimer1);
                        window.clearTimeout(alertTimer2);
                    });
                }, 5000);
            }
        }, 100);
    }
}

setTimeout function only execute once where setInterval checks on a regular time interval. For example: https://codepen.io/anon/pen/VGPYXB

The better solution could be when you adding alert message set setTimeout function after adding message or use delay function like this https://codepen.io/anon/pen/XPpJGe.