This is really frustrating. Bought my wife a second PS4 and Destiny. Ever since ROI came out we can't connect at all. Today's patch was supposedly going to attempt to fix this and it didn't change anything for us. We are both hardwired to the router. I tried setting up one of the 2 on wifi to see if that made a change, still not able to connect.
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Xbox has the exact same problem. It's infuriating.