besides getting a new emblem . you might be able to push the nuts on the sheared post flush against the door. on the emblem nuts centers are angled out for screw twisting . flatten the centers that grab the post before pushing them on.may make better connecting contact with the post. if the nuts is loose after that only thing i can think of is a clear superglue of some sort to put on the nuts and post.
That is the issue with every single repop marker I have ever seen. When we redid our 68 Camaro we bought ALL new markers for the entire car and when we went to install them, almost every single one of them either snapped off or stripped out. That was the one nice thing with our bird, it had all it's original markers from the day we bought up until she was just parted out. I left all the markers on the original panels when they were sold. I guess that's why NOS/OEM stuff is worth the expense...
my gas tank emblem was the last original emblem on the car. however about 4 months ago the colored plastic filling cracked and eventually just fell out in a few clumps. it looked like crap and had to go. it makes a great paper weight though.