This error can be shown by our integration addons with delivery services, like Mailjet, Sendgrid, Mailgun, ElasticEmail, Brevo, SMTP2Go, and Mailersend when testing the connection or even as a reason for a newsletter block due to a fatal error.
That error is not a fault of your site but needs to be addressed by your provider. The two main reasons for a cURL error 35 are:
- the server or PHP is running outdated components while the SSL protocol needs updated libraries or certificates to establish a secure connection. The provider should update the server software.
- the provider is blocking, using a firewall, the connection to the delivery service. The firewall drops the connection or replies with an invalid content making cURL to return an error: once again the provider should check the problem and unlock the connection.
The second case may show up randomly: sometimes the firewall is configured to check for “too many connections” to external sites and stop them (believing they are generated by a compromised system).
Only your provider can solve those kinds of problems: updating WordPress or your plugins is recommended but not a solution to the cURL error 35.