Look, no support
The hardest question to answer is the simplest: why make the move from Server 2003 to Server 2012?
I do not buy into the value of using the newest software as an end in itself. The end of support, however, is the obvious bogeyman and there is some validity to the fear.
New vulnerabilities won’t be addressed and your Server 2003 systems will become a massive security risk!
To run a secure IT infrastructure – and increasingly to meet the legal and regulatory requirements of many jurisdictions – you will have to pour resources into monitoring and shielding any servers running Server 2003.
Waiting to long to upgrade
The problem with a last minute migration approach is when the server/version upgrade results in problems, errors or inconsistencies with security, stability, or functional issues with your applications that require immediate remediation, and most often programmatic revisions.
Needless to say, waiting until the last minute to perform your Windows 2003 server migration is a risky proposition.