I performed my last 2003->2012 upgrade a while back. Three years? I thought I was being the stalwart on it.
Sorry, people, as much as you might say that you can continue with 2003 (of course you can, you could continue with DOS if you wanted to), there's a point at which it just doesn't make sense. When I transitioned it was hard to find 2003 drivers for RAID cards and things like that. I'm sure you have them.... for your current hardware.
When that RAID card breaks and you can't get a replacement (or you can, but a replacement server with RAID card is actually cheaper!), you'll struggle to get it across. And then you're into a 2012R2 install anyway, and virtualising what you have onto it. If you're bright enough to still have the full up-to-date system state to start from (Oh, you can rebuild the server you have with your data? Then on your head be it).
And then when you recreate your config on 2003, you'll find that much of it is obsolete and you could just use the built-in stuff in 2008/2012 to do what it does. In 2003 much of the useful stuff didn't really work well or at all. In later versions it's a core part of the OS.
I'm sure you can struggle on for another few years, with some IT guy that doesn't want to learn, with some users that don't want to transition, without spending a penny. And sometimes you can get away with that. When you can't, though, it's just embarrassing. I'm far from the "let's deploy cutting-edge just because" crowd, but there's a point at which the world has tested the software for you and written down all the quirks and workarounds and you should move forward.
As someone who's worked for schools with little money to spend on IT (including one that could not afford textbooks one year), done disaster recovery and freelance "consultancy" (yuk, hate the word) on places that are in dire need of IT help (and at least once said "I'm sorry, you need men on the ground each day, not consultants coming in and taking shots at what you haven't got, no charge for me telling you this"), I can tell you that IT is NOT a one-off expense. It never has been. If you put off the annual cost of it, you'll pay it in the future (plus interest!) in one lump sum, it's as simple as that.
And if you are large enough to have a permanent IT guy, then you're large enough to make him do his job (including professional development, future strategy for the IT, budgeting, costing and speccing out a new network every now and then), and large enough to afford an annual expense. Smaller than that, well, that's your business. But if you're running "servers" (plural) then there's really no excuse.
I'm sure 2003 will serve you well for years to come. And then the crunch point will cost you twice as much as it would have done to do regular maintenance. No different to never taking your car for service, not going to the dentist, or just leaving that leak dripping in your house because you "can't afford" a plumber.