This is a bigger issue with X-Cart than just X-Payments though another thread was told to look here. For example, 4.3.2 and Authorize.net AIM now fails since Authorize.net turned off SSLv3 support.
cflsystems' recommendation to disable SSLv3 is the generic fix but I'm surprised there hasn't been an official patch for some older versions of X-Cart, at least 4.3 and 4.4, and this thread should be moved to an appropriate area.
EDIT: The example of 4.3.2 and Authorize.net is incorrect. This setup appears to still be working fine.