Metal Gear Solid V: Phantom Pain is slowly removing support for the older systems but they still have a bit of time to enjoy the services.
Persistent online services in gaming pretty much mean portions of a game, if not the entirety of it, depending on the developers' will and ability to keep it all running. Once that's over, the game loses partial or full functionality.
In the case of Metal Gear Solid V: Phantom Pain, it will only be partially wounded when the online services shut down as you will still be able to play the single-player content. It's especially important to catch that tiny detail on the announcement page since many fans were worried the entire game would become unplayable as it requires constant internet connection.
Another highly important thing to be aware of is that the online services will be terminated only for legacy consoles - PlayStation 3 and Xbox 360.
As for the date when the online services will get axed, it will be a rollout that will happen over 13 months:
- August 31, 2021 - Purchase system goes down
- November 30, 2021 - MGO DLC will no longer be purchasable
- March 1, 2022 - Will no longer be sold on the platforms
- May 31, 2022 - Full retirement of service
This leaves fans with a little longer to enjoy the full breadth of MGS V: Phantom Pain but the immense replayability is sure to keep people invested in years to come.