I saw the message about Xbox One players having issues connecting, and I had gotten booted from the game once around the time that message first posted to Bungie.net, but in the last fifteen minutes or so (from approximately 11:40 PM PST until now (11:56 PM)), I've gotten Vulture error codes at the point at which my chosen character's ship comes into view on the screen,
The left side of the screen says, "Waiting for party stabilization," then the screen goes black after about 3 to 5 seconds, and the Vulture message appears. It's consistently happened about 4 times in a row now.
I know my profile has not been signed in elsewhere, and that my permissions to access online multiplayer gameplay has not changed, so I'm not sure why this is occurring.
I am super glad I got my 2nd Nightfall done just before this problem kicked into high gear, though.
I hope the info provided helps somehow. Cheers!
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It's just started doing it to my account too. Seems like that last update had a few more bugs than usual :-/