Microsoft will no longer be providing security patches, leaving the system open to potential new threats from hackers and malware.
Application developers will not necessarily continue providing backward compatibility of their application to legacy systems, which could cause application updates not to work on an older server.
Many applications are now being produced in 64 bit versions. Taking advantage of the enhancements that come with the 64 bit versions of your applications requires a 64 bit system.
Most new systems are built on a 64 bit architecture where most of the Windows Server 2003 systems would have been 32 bit systems. There could be issues with legacy peripherals which do not support 64 bit drivers. It is always wise to check with the suppliers to be sure that key devices are supported before you begin the conversion.
Support & Maintenance
As legacy system age, it is inevitable that components will begin to fail. The older they are, the less likely it will be that repair parts will be available. Waiting till there is a catastrophic system failure is not the best way to manage the upgrade process.
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