The certificate wasn't on the server. It was embedded in a DLL written by a developer named “S. Yamauchi” who had retired in 2007. The certificate had a hard-coded lifespan. And it expired exactly… now.
Source: LegacyCrypto.dll | Reason: System clock mismatch. Certificate expired Dec 31, 2005 23:59:59. dotnetfx365.com
— A story for the developers who keep trying. And for years after, when new hires asked why the company’s critical system was so stable, the seniors would just smile and say: “Go check the 365th build.” The certificate wasn't on the server