Recently we disabled SSLv3 support on our servers. See
http://forum.x-cart.com/showthread.php?t=70268 and
http://blog.x-cart.com/SSLv3-shutdown-Nov-19th.html
Most likely your X-Cart server does not support TLS 1.0 or TLS 1.1 and this causes the issue. Please work with your hosting admin to make sure your X-Cart server does support TLS 1.0 or 1.1