The Solution: A network issue with your console or network hardware.
Perform a cold reboot of your console and your networking hardware by doing the following:
Exit Destiny and shut down your console. Once your console is fully shut down, unplug the power supply from the console for at least 30 seconds. Unplug the hardware in your networking setup and leave it unplugged for at least 30 seconds. Start to turn on your networking hardware, starting with the modem, and working your way out to additional hardware. Plug in and turn on your gaming console and launch Destiny. Attempt to reconnect and play Destiny.
