My wife is now running into this problem, I highly suspect its because of her green card. She is Canadian, and was on an H1-B, and I am US, and until now, using online check in from Canada was never a problem. The last two weeks, her first trips as a green card holder, I've tried to check her in (after records split), and she gets this message. I haven't tried for myself on those trips, since it seems silly since we have to go to the desk anyway, but suspect I wouldn't have an issue.

Spoke to web support, who first said it is not a green card problem, but that you can't check in online from international destinations (thanks for the BS). When I called him on it, he checked and said it is random and that sometimes she may be able to check in online when returning to the US, which is also what the agent said at YVR last week. Was hoping this could be solved like the passport problem, by scanning in at the airport (and having it added to your profile, but there doesn't appear to be a place to enter it (or am I missing a place where this can be entered). Frustrating if this isn't able to be corrected and airport check in only for the next 3 years.