FYI, This was fixed around 12 Feb 2018. I didn’t realize it at the time, but the third item on the bullet list,
We update who is invited to events more quickly
also resolved this issue. Any time you view an event, it “refreshes” who is invited to the event. Here are some more things that will refresh who is invited to the event:
- Creating/Updating an event
- Viewing the event’s details page
- Sending event invites/reminders
- Sending the newsletter (All events in the newsletter will be “refreshed”.)
The last two are especially nifty because they happen automatically behind the scenes. So if you create your events in May, schedule them to send invitations 2 weeks ahead of time, and then enter a bunch of new members in August, they’ll all get the right invitations and newsletter content without you having to do a thing. 
They’ll then be able to RSVP directly from the invitation, and life will be peachy. 