Hi,
Well, first, when the payment is declined, in most cases (it depends on the payment gateway), the customer is presented with a link to go back to the website. If you have the "clear cart after order is" setting set to "confirmed", the customer will normally be back on the checkout with his cart and we'll be able to purchase again without you doing anything.
And now to answer you, you first need to activate the "Payment of orders not paid immediately" setting in the HikaShop configuration.
Then, in the System>Order statuses menu, you need to enable the order statuses under the column "unpaid" for the statuses you want to allow the customer to pay for.
At that point, if the customer accesses his orders history on the frontend of your website, he will have a "pay now" button for each order in one of the statuses enabled for the unpaid column.
And if you edit such an order in the backend and click on the "email" button at the top, the email will contain a payment link automatically.