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The main issue I see in the photo is that the posts are way too small for a gemstone that big - you're always going to have this problem if that's how they make all of their studs. All studs of this type are glued in, but there is a hole drilled into the bead and a post should be wide enough and long enough so that there is something for the bead to hold onto when glue in place.
I hate to say it, but I wouldn't be surprised if this happens again with the new pair - design flaw!
If you really love the earrings, I would take them to an experience jeweller and have them put a better post in both studs. It'll cost you to do so, but at least they will last.