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This has nothing to do with PSN itself.  Either a game allows online play via dedicated servers hosted by the publisher/studio, as is the case with Demon's Souls, or it uses a peer to peer connection, using a player's console as a host in lieu of a server.  PSN only comes into play when storing the game's trophy information, which is something inherent to each PSN member, not the game, and thus wouldn't disappear with Atlus' abandonment of its servers.

It's a common misconception that services like PSN/XBL are used as a base for online play.  In reality they are merely gateways that let ps3s/360s talk directly to each other.  The task of providing online play is on the shoulders of the makers of the game, who either provide servers (which cost money), or set up a P2P network (which doesn't cost a dime once in place and theoretically lasts forever).  The only things that cost Sony/MS money are the storage and retrieval of a member's information, like trophies/achievements, friends lists, games you've bought, etc., plus the perpetual network that let's people access this information at any given time.

Maintaining servers for a game like Demon's souls is very expensive, Atlus doesn't have that kind of budget. Let's face it, they're no Square-Enix.

demon's souls 2 anyone?