UPDATE: It now looks like P.T. is being stripped from the Sony servers with people now unable to download it from their library even if they already owned it. Previously Konami has only removed the demo from the Store, making it impossible for new people to get it, those who already had it could still access it. That looks like it's changing.
It's being reported that so far only the US has been affected, with the UK currently still able to re-download the game. It's an extremely odd development because usually even delisted content is usually still available for those that bought it. I suspect the fact that P.T. was free has enabled Konami to kill it in a way that wouldn't have been possible if it was a paid-for product.
UPDATE 2: Some users who downloaded P.T. in Germany are seeing an expiration date on their game information (including Minecraft musician C418). That seems to be because P.T. was technically distributed as a PS Plus Instant Game Collection title in Germany, and the expiration date simply indicates the end of the user's current subscription.
If your subscription expires, P.T. should start working again as soon as you renew, like any other Instant Game Collection offering. "Should" being the operative word there, as this entire end-of-life process has been utterly bizarre. Thankfully, P.T. was just a free download elsewhere, so most folks only need to worry about keeping it on their PS4 hard drives.
ORIGINAL STORY: So after all the kerfuffle surrounding PT being removed from the PlayStation Store and the fact that people are already trying to eBay PS4's with PT still on it, it turns out you can still download the damn thing.
Look, here it is slowly drip-feeding itself onto the only bloody PS4 I could find that didn't already have it downloaded:
The catch here obviously being that it's being accessed from the PS4's library, after previously being downloaded pre-removal from the PS Store.
After Konami announced it was being removed from the Store yesterday, everyone apparently went into panic mode and downloaded it. EVERYONE. We must have about 10 PS4 scattered around the building here and it took me 40-odd minutes to find one that hadn't scooped it up like bottled water after a hurricane warning.
It looks like it's a similar deal to OutRun Online Arcade, which was removed from the Store after Sega's licensing deal with Ferrari expired - if you own it, you own it, and can still access it. New people can no longer get it but if you already downloaded once before, you still can. I'm guessing while Konami no longer want to promote it now the full Guillermo del Toro/Hideo Kojima Silent Hills project is cancelled it's still on Sony's servers and there's probably a legal issue relating to digital rights, even if it was free.
Basically, if you didn't care enough to have downloaded it before it was pulled you won't care now, but if you did care, you're all good. No need to horde it on your machine.