I doubt it's getting shut down at all.
Reason being, PS NOW. The PS Now games use the same servers as the PS3 games. And at the very least they'll need those to keep games populated.
Sure, some individual games got shutdown. But that happened with the 360 and Wii too. In fact, even the 360 online won't get shutdown. The Wii was the only one to just shut everything down. But then again, they didn't have much of an online network to begin with.
This isn't like the switch from the PS2 to PS3 or Xb to Xb 360. The PS3 and 360 are totally entwined in their respective networks.
Now, in terms of actually MAKING games, sure that may stop. But the ecosystem itself won't because of their PS Now ambitions.