I have to deal with this crap multiple times daily. In fact it just did this to me twice just now in less than 10 minutes. My internet has always been perfectly fine too. It's always with this game that I ever have problems.
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It seems to be only this game for me too, I rarely have connection issues in any other game. Hopefully they aren't banning people for poor connections, I can handle a kick but a ban would be somewhat ridiculous. BattlEye's FAQ does state they don't ban for poor connections,only kick. I hope that holds true in Destiny as well.