I am having the exact same issue, luckily I only get caterpillar. What makes is so annoying is that I am 100% every thing on my end is working and up to spec....
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Same issue constant d/c and don't talk me it's a problem at my end because it's not. Something is very wrong with bungies servers or game. Strikes are pretty much unplayable for me as it stands, I get d/c out of most of them. The rest of the game runs fine. Sort it our Bungie, online only is alright if you don't screw it up like you are right now.