I am supporting a Classic ASP application that connects to a payment gateway via HTTPS. Up until recently there have been no issues. A few days ago the latest updates were
This is probably a ServerFault.com question really, after all if the code is working fine then its not a programmatic problem.
However I would try a couple of things. First try using a the ProgID "MSXML2.ServerXMLHTTP.3.0", in some circumstances MSXML3 will behave differently depending on which ProgID was used to instantiate the component. Also update from other sources like your anti-virus supplier (Sophos had this problem) can break MSXML installs.
Another ProgID to try is "MSXML2.ServerXMLHTTP.6.0" after having installed MSXML6. If the problem is with an update to the MSXML3 core then perhaps the MSXML6 core doesn't have the same problem.