Check if they’re trying to download via the Etsy app, which is not possible. They have to use a regular web browser, and to be signed into Etsy with the same account as they made the purchase under.
There are some other nuances related to downloading here, but those are the 2 big sticking points. One other is that the email on their Etsy account is no longer the one they usually use, so they don’t receive the payment confirmation email with the download link.
