We’re having this problem as well, it started last night on Munition Acquisition and no matter what we tried we couldn’t get it to even offer the prompt for other members to join.
It’s continuing today with Breaking the Bone Ship. No matter who enters first, who’s in the party, if we log out, the prompt isn’t offered.
Edit: Wanted to add we’ve never had this issue before all the way through to these quests yesterday.