EA's CEO basically said on Polygon that the primary reason to shut down The Sims Social and SimCity Social was that the games stopped being as fun without enough players to keep it going. That's fair, new Sims Social or SimCity Social players that stumble across these games would have sub-optimal experiences and it makes sense to shelter them from that. But what about the players that want to keep playing, diminished experience be damned? What about people who spent lots of money in game and want to be able to drop in and see their nicely furnished home or custom city now and then for old time's sake? This wasn't done to make sure they had the best experience. I suspect it's really a complex cost-benefit analysis that led to the decision.
First off, games aren't free to run. Servers aren't free, customer service and community management aren't free. Tracking costs, revenues, royalties, licensing, and taxes is an expensive hassle. You need all of these things to keep a game online with a minimum bar of quality for players, but the good news is that these costs are relatively small; incremental, really, if you're going to be running other games on that platform anyway. These things add up fast though, I know.
Second, even if you don't have staff dedicated toward maintenance you still need some engineer time to keep the game running because the platform changes underneath you. It's a pretty safe bet (for any game run as a service) that a couple times a year your platform or a partner SDK are suddenly going to stop working and lose "backwards compatibility" with your game. That means you can't just leave a game running and forget about it, even if it is making enough money to pay for itself.
Last, if you have a different, new game then you can shunt your players over there. Maybe by forcing them into another of your games you can make more money or get more engagement from them. Heck, I'm still playing Battlefield 3 and Modern Warfare 2... if they suddenly stopped working then I'd have to go buy a new shooter.*
*Actually, I'm going to do that anyway, but you get my drift.
Still, players have paid for content in that game. They love that game, and they want to play it some more. And for games that run as a service, it's not like they can pop in the cartridge one day and fire it up for old time's sake. When it's turned off... it's gone. Sometimes all the money you spent is gone too, though some companies allow you to transfer some or all your investment to a new game.
I'll be honest, if a few years from now I'm spending 10 hours a week just keeping Sinister Dexter running for $200 after expenses... well then I'll vote to put the game to sleep. But if the game continues to at least pay for itself and the people it needs to keep it going, then I'd really like to see it live as long as there's a player who does too.