The only reason why it would redirect back to the checkout page would be if it failed validation. Are you able to reproduce the problem? The key would be to see what they are entering into the checkout form so that you can reproduce the problem, then you can debug and find a solution.
I see your checkout page isn't displaying server side errors, so in order to see which server side error is being triggered you can write the main session variable: <?php echo($_SESSION['WAVT_confirm_362_Errors']); ?>
That will allow you to see which error is failing and make any necessary adjustments.