Running an OS in a production environment means that you need to be able to recover it when something goes catastrophically wrong.
Being able to rebuild a server isn’t just about having the OS on hand, you need to have access to the drivers and applications as well. While you might plan to perform a full server recovery using your backup solution, you need to be able to fall back to performing a clean install of the server, driver, and applications should your backup images and data for some reason be unrecoverable. Which, if you perform regular server recoveries, you know is something that happens more often than anyone is really happy with.
Remember that just as application vendors aren’t going to support Windows Server 2003 forever, backup and recovery solution vendors aren’t going to support backup and recovery of Windows Server 2003 servers indefinitely either. There aren’t many backup vendors around who still support backup and recovery of computers running the Windows 2000 Server operating system.
When you stay with Server 2003, you need to also stick with all those applications that support that Server 2003 ecosystem. This doesn’t just mean sticking with the applications running on the server, but also versions of the virtualization platform that host the server, device drivers used by the server, and monitoring and backup solutions that allow you to maintain the server.