'Probably best just say here, before things get confusing:
EVE Online's servers are under massive, continues stress. It's the largest single game world on the planet and operates across hundreds and hundreds of smaller blade elements operating in sync. That's the reason for Trinity being shut down daily; it has much higher maintenance needs than most games' servers.
That being said, as a result of the above CCP have had reason to invest a lot into technologies and systems that minimise downtime during maintenance, because they don't have the luxury of just shutting down for a couple of hours a month as most big-name MMO's do. That, combined with the bladed server architecture that allows individual elements of the game servers to be offline while others are active, is why they're able to go through regular maintenance and even minor patch deployment inside half an hour (used to be more than an hour) and think that one day, they'll be able to perform maintenance without even needing to take the game offline at all.
So.. yeah, just to nip any 'but EVE does it in half an hour' arguments in the bud. Besides, that same architecture has a lot to do with their big updates generally disabling the game for 6-36 hours at a go. Well, that and that time earlier this year when one of the blades caught fire when they turned it on again >.>
Not that it wouldn't be awesome if other MMOs took to using blade setups and unsharded worlds, of course, but I guess that's a long way off for games whose zones aren't infinitely large and don't generally have terrain to render.
And good lord you think this is bad? You should see the cries for refunds when those big patches are deployed, on their forums. 'Course the EVE forums are a hellhole at the best of times... yeah okay I'm rambling now.
TL;DR: CCP spend lots and lots of money and research on being able to get maintenance done sharpish. Most big MMOs don't. Therefore 'EVE can do it, so should FFXIV' = bad line of argument, don't bother.