The occurrence of the “cURL ERROR 28: CONNECTION TIMED OUT” error might occur during the activation, verification, or deactivation of update keys within Gpl WordPress Update Manager, or when attempting to update plugins or themes.
 
WordPress utilizes a function called cURL, specifically the wp_remote_post() function, to establish communication with external websites. This function is essential for verifying update keys and executing updates.
 
Successful communication between your website and ours is crucial. We require your website to convey the update key you’ve entered so that we can authenticate it within our records. Subsequently, we send a response back to your website to activate the key.
 
A cURL timeout often indicates a blockage in communication between the two websites. This blockage might occur due to firewalls or other security measures implemented on the server, hindering the exchange of information.
 
The first thing to do is go through this list. Your hosting support should be able to help you with most of it.

• Make sure your server is running a recent version of PHP and the cURL library.
• Try increasing your PHP memory limit.
• Try increasing your cURL timeout limit.
• Ask your host if there is some limitation with wp-cron, or if loopback is disabled.
• Ask your host if there are firewall or security modules (e.g. mod_security) that could block the outgoing cURL requests.
• Install the Query Monitor plugin and check the status of the HTTP API Calls in the admin page where the error is displayed.

If the solutions mentioned earlier do not resolve the problem, it’s advisable to contact your hosting support. They can verify whether your server can establish unrestricted cURL communication with our server.
 
Once they confirm that there are no limitations, feel free to reach out to us with your server’s IP address (the origin of the request). We will then ensure that your server’s IP isn’t banned on our server, although this situation rarely occurs. Our server consistently handles numerous cURL requests successfully on a daily basis.
 
This article also has some great information on this specific error and may help you/your hosting support team debug the issue.