My plugin uses the Envato API to verify license in order to use.
Customer emailed me externally and says he closed his Envato account so now the plugin won’t work for him. He did have a License Certificate but when I try to verify Envato API returns “No sale belonging to the current user found with that code”.
What should I do in this case?
Most of the cases, Envato doesn’t terminate the accounts, it’s been probably disabled by the team for some reasons.
You don’t have to do anything, tell the client that he/she needs to verify the license to use it. That means, if he/she wants to use it, he/she may activate the account by contacting Envato or purchase another copy
Yeap! 
Point them to Envato Support. This seems really fishy to me. Why would they close an account their using Licenses on?