For this question, consider the potential negative impact of sending the user off to google for a voucher code only to find expired or duff codes, which would snag and delay them significantly as well as possibly resulting in a lost sale.
Are such negative impacts resulting from displaying a voucher code field during checkout when there are no active codes available sufficient enough to warrant only showing the field if there are active codes available ?
I would suggest hiding it if there are no valid coupons which can be applied to it.
As per this article,
27 % of users abandoned carts to go search for a coupon codes
and if there are no valid coupon codes available, there is a possibility you might lose your users as they might not return.
That said, you can use that space to get people to sign up for your newsletter and increasing your reach by offering them discounts via email as shown by this article. To quote the article
Alibris does one better by providing the ability to enter an email address right on the page, as opposed to Office Max which makes you hunt for the email subscribe area.
On reflection of what Marjan Venema pointed out, It might be better practice to show that there are currently no active coupon codes which the user can potentially use as that would reduce the confusion about if a old coupon code found was valid or not.
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Consider a different approach: dodge the problem. If you always have some kind of discount available, even if it's only 1% and posted right on the screen as "If you don't have a code, type ONEPCT to receive a discount!" you'll always engage the user. Your customers won't feel as cheated that they're missing out on something that other people get.
As a bonus, your UX remains consistent.
Personally, I think that, if your site accepts discount codes, you should always show the field where the customer is supposed to enter them, for a couple of reasons:
Now, that being said, I also think there is room for improvement, in regards to this specific user experience (like you suggested, it can be frustrating to a customer to go off looking for a coupon and not find one). Personally, I wouldn't mind seeing a message by the field, indicating that there are no currently valid codes (maybe include in it a link to the "coupon sign-up process", that Mervin mentioned) . . . potentially even have the field disabled, as well. But, if discount codes are something that your site supports, I think it's pretty important that the customer can see that field, in the same place, every time that they go through the checkout process.
If you really want to be radical, hide the discount / voucher code input and automatically apply the discount to qualified customers. Give them some indication that they've been saved X amount and why and watch customer delight increase.
