Just to point out nearly every game since release of xbox360 still has online so why is that EA truly need to shutdown servers all the time? Its not too hard to see that they dump their games and run unless you live in the land of naivety. Look at Crysis 2 for an example the multiplayer is shoddily done and there has only been a patch to reduce xp. Looking at NFS: Carbon and Crysis 2 I don't think they get around to fixing broken achievements either. Looking at the sport franchises as per topic a lot of features involving achievements were discontinued within months of game launch. Sure it costs money mainly because lackluster sales from lackluster games and poor use of servers.
I never said they need to, only that it's more profitable for them to.
As for dropping their games and running -- their games' multiplayer wouldn't last 6 months due to server problems if they did that. Just because a game's multiplayer sucks, or because they don't put much
money into their maintenance of the servers, or even a complete lack of patches, does not mean they don't spend money. Granted, they probably spend the bare minimum necessary to keep it running, but they still spend money. Crysis 2, and even all the Battlefield games up to, and very likely including, Battlefield 3, and pretty much every other EA game, would have had the multiplayer shut down long ago due to the servers simply not working right. They might not spend much money, but the multiplayer wouldn't exist if they didn't spend any.
I don't think you quite understand what server administration, especially in this industry, consists of.