On mine, the recessed hole broke out. I epoxied a metal washer in it's place to the "shell". The screw holds the washer against the door...while the shell is epoxied to that washer (if that makes sense).

If starting with a replacement, considering running epoxy (plastic compatible) around the outer edge of the recessed hole. By that, I mean on the backside of the trim piece. It might help to use a washer on the outer side (depending on how yours are splitting out). I would also inspect the retainer that goes in the door -- that you screw the trim piece into. Seems odd you are breaking so many of these trim pieces! Maybe your mount is not flat?

You might also fill the entire recessed mounting hole with epoxy then redrill it. Your screw will sit up a bit higher -- but you'll have a thicker trim piece-to-door mounting point.

Otherwise, you could probably have a metal fabricator duplicate most (if not all) of the trim piece. Maybe a "u" shaped piece to start (with the hole in it), then weld top/bottom "sides" to it. To that, cut off and bond the outer trim square for a finished look? That's if you can't get anything else to stay....you brute! :-)