it says:
"It seems that your blog cannot contact the license validator. Ask your provider to unlock the HTTP/HTTPS connections to http://www.thenewsletterplugin.com
http_request_failed - cURL error 28: Operation timed out after 2000 milliseconds with 0 bytes received"
How to resolve this error? And what is the impact for my sending email newsletter?
There are no impacts only the updates of the addons won't be available directly from your blog, but you can always download them from your account page in this site.
The connection timeout should be analyzed by your provider to understand is there is a block on your side.