This problem was caused by the SMTP_Block that is enabled in the server. It means that all the emails that are going out from the server are blocked especially special programs like Squirrelmail, Mailcube, and Horde when you use Webmail and our SupportCenter where it is using the SMTP of the server. The SMTP_Block is already enabled when the cPanel is updated.
The solution to the problem is to disable the SMTP_Block by using the WHM of the cPanel. You can see this by clicking the ConfigServer Security&Firewall of the Plugin. Then click the Firewall Configuration at the right side page. Search for the SMTP_BLOCK and change the value of the box to 0 (ZERO) to disable the SMTP_Block.
But by disabling the SMTP_BLOCK (or WHM SMTP Tweak option if you don't use csf) option. In doing so, you leave yourself open to exploited scripts sending out spam while bypassing exim.
The Other solution is to Enable or check the use Sendmail. But your php has to be correctly configured and support this type of sending of mails.
Source: http://support.qualityunit.com/knowledgebase/supportcenter/troubleshooting/smtp-failed-to-connect-socket-connection-timed-out-code-1-response.html(http://support.qualityunit.com/knowledgebase/supportcenter/troubleshooting/smtp-failed-to-connect-socket-connection-timed-out-code-1-response.html)