Aside from the fact that your 2003 versions of Windows Server are probably running on outdated equipment and not performing up to today’s standards, there are three things that can put your operations in jeopardy if you don’t upgrade soon.
The world of security breaches has changed, and even though you’ve faithfully applied every available patch since 2003 (you have, right?), the 2012 version is inherently more secure. Hackers know everything there is to know about Windows Server 2003 because they’ve had a decade to explore it and develop ways to get past its inherent weaknesses. One of those that has been resolved is the traditional ROM-BIOS boot process that leaves a space for injection of malicious boot code updates.