Have you identified that that every SSL connection (from all clients) to a specific problem server is failing? Is it possible that the problem is only experienced by certain clients, regardless of which server they are hitting? If so, the problem may lie in the certificate validation steps taken by the client. Perhaps only certain clients are experiencing this validation issue, and others are not. Do you get any warnings on the client side when browsing from IE? (aka "There is a problem with this website's security certificate.")?
You can use the CERTUTIL command and the -verify option to investigate if validation is part of the problem. First, browse the site from a client experiencing the problem and save the public key for the cert in question (see pic). Next, invoke the certutil command:
certutil -verify bad.cer
There will be A LOT of text in the output from -verify. There will be a summary at the end with a friendlier message (example: Verifies against UNTRUSTED root). Reply for help with interpreting the output if needed.
Certutil -verify example
