Well it appears I've asked about something that happens to others as well. Cindy, I think you're on to something there. I've noticed I'm not getting the group notices from larger groups. I've even gone back now and checked several of them with your thought in mind, and sure enough I do get group notices from smaller groups more routinely than large ones (rarely, if ever).
Sounds like something I'll just have to live with.
Reason I asked in the first place is because a new group I just joined sends out a deal almost daily, but at random times. I have not gotten one of their group notices emailed to me while I've been offline, and have missed the deal a couple times. Was really hoping to find a way to be sure the group notice gets emailed to me while I'm offline, but the group is in the thousands, so it's probably just not getting it sent to me.
I have a notion that even in-world group notices are not working for every member of large groups even if you're online. I'm going to start watching this more close. Not that LL will do anything to fix it, but it should at least be mentioned somewhere, and large group owners should know that their notices might not be reaching all intended recipients.