Are you using TWC for internet? I'm having the exact same issue.
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MediaCom, but it's not just happening on Cable ISP. At first is was destiny servers timing out on the last hop. I believe it is a bug when they tried to fix something in the latest patch. That I believe is causing the application to bug out and crash the PS4. Again, no other online game is having the issue, bad news is if Destiny Crashes you have to reboot your PS4 for it to work. Buggy coding, most likely.