"You have lost connection to the Destiny 2 servers.Your permissions to access online multiplayer gameplay may have changed or your profile may have been signed in elsewhere." No one has my account other than my PlayStation 3's, so it's not that. I can play other online games, so it should not be a network issue. If I got banned for whatever reason then I'm going to be mad because I didn't want to spend $80 to get banned for not cheating. Also I get disconnected from the game world WAY too often (about 5 times a day). This is definitely your servers because like I said, all my other online games work perfectly.
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That has happened to me a few times since Destiny 2 released. Turn off your PS4, unplug both it and your router and leave them unplugged a few times, plug them back in and you should be good to go. Once I had to restore licenses as well for some reason, but those steps have fixed it for me every time.