Php Curl Connectin timed out

I have worpdress plugin which communicate with my production site https://mysite.com via curl.
Here is the curl code:

   $vars = json_encoded(
                array(
                   //some params
                  );
   );

    $headers = array(
        'Accept: application/json',
        'Content-Type: application/json',
    );

    $ch = curl_init();
    curl_setopt($ch, CURLOPT_URL, "https://mysite.com/myapi");
    curl_setopt($ch, CURLOPT_HTTPHEADER, $headers);
    curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
    curl_setopt($ch, CURLOPT_POST, 1);
    curl_setopt($ch, CURLOPT_POSTFIELDS, $vars);
    curl_setopt($ch, CURLOPT_SSL_VERIFYPEER, 0);
    curl_setopt($ch, CURLOPT_SSL_VERIFYHOST, 0);
    $result = curl_exec($ch);

    var_dump(curl_error($ch);

It works fine for all wp sites which use my plugin, but suddenly it stop working for just one site:
and curl_error() returns this:

Failed to connect to mysite.com port 443: Connection timed out

Also my plugin is not on the wordpress repository, it’s placed on https://mysite.com/plugin and my plugin use hook “site_transient_update_plugins” to check for available update. This also doesn’t work anymore and they don’t get message about update available anymore.

So I guess that they changed something on their server which cause this problem, and I just cannot find what can cause this.

Also I am not 100% sure, but connection take about 300 s before it throw this error. And 300 s is default value for CURLOPT_CONNECTTIMEOUT.

So any suggestion what can cause this behavior will help.