What is an advantage or disadvantage for not upgrading database server?

If you don't:

• it will be unmaintainable at some point because of OS, version, patch, whatever
• hardware failure may force an upgrade at the wrong time

What you gain:

• older code can be simplified with new constructs (eg ROW_NUMBER)
• far better error handling (TRY/CATCH)
• engine improvements: most queries will run quicker on a later version

MS don't support it anymore either

GBN is spot on with his analysis - I'd just add that something that can buy you time, if your company has the technology, is to virtualise this legacy database server, either as a new build or as a clone/P2V. This will buy you time in that you'll be better protected against hardware failure.