You have been loading CF-7 form using ajax
by that means required scripts for that form never executed for that. And, because of that thing your form not working as it was expected to be.
You have to re-initiate
the scripts of CF-7 for the particular form. Here, is the updated PHP code.
Now, your ajax will be:
<?php
function _myConfirmHandler()
{
if(isset($_POST['vehicle_no']))
{
$vehicle_no = $_POST['vehicle_no'];
$email = $_POST['email'];
echo do_shortcode('[cfdb-table form="season parking form_copy" show="your-name,mail,your-platno,your-location" filter="your-platno=' . $vehicle_no . '" headers="your-name=Name,mail=Email,your-platno=Registration No.,your-location=Parking Location"]');
// Display the Form
echo do_shortcode('[contact-form-7 id="6959" title="Payment season Form_Post"]');
?>
<script>
jQuery('.wpcf7 > form').initForm();
var urL = jQuery('.wpcf7 > form').attr('action').split('#');
jQuery('.wpcf7 > form').attr('action', "#" + urL[1]);
</script>
<?php
}
wp_die();
}
?>
Update:
initForm is no longer present since CF7 5.4
Thank You @Chris Pink