This may be due to the reason that the Envato API server may be down at the time when you try to activate the license. You may try after few minutes.
There could be another reason that your server does not with installed cURL library or may not allow running the WordPress function wp_remote_get(). You can check if all server requirements are fulfilled here https://yourwebsite/wp-admin/admin.php?page=wpshapere_help
Please read the following article to know how to enable cURL in your server if not installed https://askubuntu.com/questions/259681/the-program-curl-is-currently-not-installed or contact your hosting provider to ensure that your hosting account is installed with cURL module.
If none works, kindly open a support ticket along with your WordPress admin login details so we can manually validate your purchase code. Please ensure that you have enabled the plugin editor and file writing permission for the plugin editor before opening support ticket.