Virtually no review site will remove a negative review just because you asked it to. If it did, who would trust its reviews? However, most sites that post user reviews will correct, redact, or remove content that contains factual errors or lies. There may even be a legal obligation to do this, in some jurisdictions. You can’t just point your finger and call someone a liar, though; you must provide a good reason for the site to go back to the reviewer to ask for more details. So dispute every fact in the review and ask for proof of the claims. Ask to see a copy of the receipt, or provide a tracking report from the shipping company that shows the product was delivered—ask for proof and provide proof. Since the reviewer deleted his account, he probably cannot be contacted to validate his claims, and you may be able to have the review deleted on these grounds. Amazon, for instance, has in the past removed negative reviews if the reviewer deletes his account or fails to respond to inquiries from a seller.
Make sure you do this under the pretense of good customer service. You want to resolve the issue with the customer, not just nuke every bad review you find. Even if your true focus is removing that review, keep in mind that if you are successful and the customer is still upset, he’ll just go somewhere else and post his review plus a follow-up that paints you as a vindictive and predatory business. When it comes to online reviews, if you fight fire with fire, everybody gets burned.